IT is an idea not universally applauded. Even the liberal magazine, New Republic, has derided the Democratic Party's ''femagoguery,'' as it has called the ''noise and commotion over the notion of a Second Lady.''
But somehow the proposal of nominating a woman for vice-president does not go away. First proposed by political activists - long before it was certain who the Democratic nominee would be - it has begun to reach the grass roots.
Rep. Patricia Schroeder is concerned that many Americans may now expect the Democrats to name a woman. ''I'm amazed when I talk to people,'' says the Colorado Democrat, who frequently shows up on the list of possible running mates. She is concerned about a ''reality gap,'' she says, and the sense of disappointment that may occur when the vice-president is chosen, and the public discovers that he is a man.
Although virtually no one expects the Democrats to name a woman for its 1984 ticket, some political strategists maintain that such a move could be a key to defeating President Reagan in November. The reasoning is based on participation.
Since the 1960s the percentage of eligible voters who cast ballots for president has been dropping. If the Democratic Party can bring these no-shows into the polling place, then it can beat the Republicans because, so the reasoning goes, the new voters would lean toward the Democrats. And a woman on the ticket might be just the drawing card the party needs.
''It would make a difference to women,'' says Ann Lewis, political director of the Democratic National Committee, who adds that voter turnout is a major priority with Democrats this year.
''It's much too early to say it's serious,'' says Edward F. Coyle, director of Independent Action, the political action committee founded by Rep. Morris K. Udall (D) of Arizona. But he says that if the Democratic nominee is a woman, it would energize people. They ''would have to take a second look. It gives the campaign a new edge.''
Roger M. Craver, whose direct-mail company raises funds for several liberal groups as well as for the Democratic National Committee, says this is the year Democrats should put a woman on the ticket. ''I think they would be helped in ' 84; I think they would be helped far into the future,'' he says.
IF a woman were chosen, she would attract more urban voters, who are also prone to vote Democratic, he says. Looking to the future, Mr. Craver notes that women are becoming more important to fund raising, and they already comprise the majority of small givers.
''I think the party and the candidates are taking this very seriously,'' he says.
If so, the person whose name appears most often is a former assistant district attorney from a neighborhood best known as the home of television's Archie Bunker. She is Rep. Geraldine A. Ferraro of Queens, N.Y., only five years in Congress and already one of the brightest political stars in the current Democratic galaxy.
In her relatively brief congressional career, Mrs. Ferraro has plunged into national party politics as well as into the leadership of the House. Her background is an appealing mix, some Democratic insiders say: the tough image of a prosecuting attorney in a big-population state combined with being a woman and having Italian ethnic roots.
Moreover, she is not backing away from the call to national politics. In the tiny ''kitchen'' of the congresswoman's hideaway at the Capitol, she is asked if she has tired of the vice-presidential speculation.
''Are you kidding?'' she says. ''No. I think it's very exciting, for several reasons - one of which is that people are no longer hiding behind their hands and giggling when they talk about a woman for national office, and I think that's wonderful.''
SECOND, she sees the discussion as highlighting the ''plight of women in this country.''
''And third, quite frankly I'm enjoying the fact that I'm getting a little more publicity. . . . If I decide to run for the Senate in 1986, it's helping me out.''
The nominee for president will make his decision not on any desire for symbolism but on the basis of cold, hard reasoning, Mrs. Ferraro reckons. ''I think the vice-presidency's too important an office to deal with it from a symbolic point of view, and I also think no one is going to give it to a woman just because she's a woman,'' she says. ''It's going to be because that woman is going to be able to bring a constituency to the ticket that they feel they absolutely need.''
Representative Ferraro has demonstrated enough political skill that her conservative district forgives her her liberal leanings and sends her back to Washington with generous vote margins. Although she spends weekends back home, she manages to pack her weekdays with enough of the right kind of activity to be noticed.
If there is one description that her colleagues give her, it is that she's a worker. ''She's a workhorse, not just a showhorse,'' says fellow New York Rep. Thomas J. Downey (D). ''I think she's one of the most effective women - one of the most effective members - in Congress,'' he adds.
''It's hard being a woman in the House of Representatives, because there aren't many of them, and a woman is always viewed with more skepticism,'' Representative Downey says. ''There is more to overcome, and she has.''
This assessment is seconded by Rep. Gillis W. Long of Louisiana, chairman of the House Democratic Caucus, a group that has twice elected Mrs. Ferraro secretary.
Representative Ferraro has been visible almost since entering Congress. In 1980 she delivered the keynote address at the Democratic convention. She is quick to agree that she has been handed some of her breaks. ''Absolutely,'' she agrees, adding, ''I think I've made a couple of good breaks myself.
Her one failure was her bid to join the powerful Ways and Means Committee. She was turned down, largely because New York was already represented. Instead, she won a seat on the Budget Committee, where as a newcomer she made a mark in budget areas affecting women.
Meanwhile, Mrs. Ferraro did not give up on her effort to put a Democratic woman on the tax-writing Ways and Means Committee. She backed Rep. Barbara Kennelly of Connecticut, who won a seat. The fact that Mrs. Ferraro lost didn't dampen her support for helping another woman succeed, Representative Kennelly says.
Mrs. Ferraro is a ''woman for all seasons,'' adds the Connecticut Democrat. ''She has three children, a happy marriage, and she was a prosecutor in the district attorney's office, which was tough work.'' Of all the women mentioned for vice-president, her name pops up the most often ''because she's the one who passes all the tests,'' Representative Kennelly says. Congresswoman Ferraro will have a chance to build her national reputation as chairwoman of the Democratic platform committee, a visible role that will take her to six cities for hearings.
If Geraldine Ferraro is the Washington name most often spoken, then the outsider most named is Dianne Feinstein, mayor of San Francisco for five years and possibly the best-known Democratic woman in the United States.
A year ago her name flashed across the public mind when she faced a recall challenge from an extremist group, the White Panther Party, which objected to a city gun-control ordinance. She survived the recall election handily, and the momentum jetted her through her reelection last November.
The election victories have also aided her national reputation, so that virtually every interviewer nowadays finally arrives at the question of the vice-presidency. She says she's weary of the question. ''I think she's very flattered by it, but she simply doesn't take it seriously,'' says press assistant Thomas Eastham, who accompanied her earlier this year to the United States Conference of Mayors meeting in Washington.
Asked what would happen if the party drafted her, Mayor Feinstein responded with, ''I couldn't imagine it,'' during a session of the women's caucus of mayors. ''I just won reelection. I am not a candidate for vice-president.''
''In our party it's been the nominee that selects the running mate,'' she notes in an interview.
But, nonetheless, Mrs. Feinstein took time out in Washington to speak to the Woman's National Democratic Club which had all the earmarks of a national political statement. Her topic was the federal deficit and the sins of the Reagan administration in cutting social services while ''tolerating wastefulness and inefficiency in military spending.
''If we don't talk about the deficit now, we will talk about little else for years to come,'' she said in the speech.
A longtime activist in city politics, Mayor Feinstein was early identified with reform and environmental movements but has now picked a centrist position, and she has been known to anger the politically active homosexual community of her city.
Mrs. Feinstein, who attended Roman Catholic schools but later chose the Jewish faith of her father, stands as one of the most striking and dynamic leaders on the Democratic roster.
Mayor Feinstein will be certain to have some of the national limelight next July when her city hosts the Democratic convention.
Even more reluctant to be seen as a possible vice-president is her fellow mayor, Kathy Whitmire of Houston, the young accountant who has weathered various storms, including a hurricane and a police mutiny, to win reelection in that Texas city.
Her concern, in fact, is more that big-city women mayors are disappearing. She and Mayor Feinstein formed the women's caucus of mayors because ''so many of the women who had served as mayors of significant cities were retiring . . . or being defeated,'' she says.
THE first woman mayor - or citywide officer - of Houston ticked off the names of cities, from Chicago to Austin to Phoenix, that have lost women mayors.
Once active in the equal rights movement and on other women's rights issues, Mrs. Whitmire holds, ''I think we've done much better in public life than anywhere else, or we wouldn't even be talking about the prospect of woman vice-president.''
Moreover, Mayor Whitmire says that women ''as a category do not bring anything different to a job.'' Instead, she says that an officeholder coming from the outside of the established power can make more reforms.
When Mrs. Whitmire took over as mayor, for example, she opened up city bidding to more firms and dispensed with the tradition of hiring city department heads from within the bureaucracy. She brought in the first black police chief, from Atlanta. ''That has been one of the best decisions I've ever made,'' she says.
But Mayor Whitmire credits the fact that she came from outside the city's establishment ranks, not her gender, for the changes.
Among those who differ from that view is Rep. Corinne C. (Lindy) Boggs, a Louisiana Democrat, who is also named as a possible vice-president and whose varied political career began with being the wife of the late House majority leader Hale Boggs Sr. Although elected to fill his vacancy in 1973, she continues to identify herself as ''Lindy (Mrs. Hale) Boggs.''
She is in many ways a blend of the new and old. Prominently displayed in her office is a model of a National Aeronautics and Space Administration telescope, soon to be sent into orbit. It is a symbol of her fondness for the US space program. And among her proudest moments in Congress is the time she inserted language to protect women from discrimination in a fair-credit law.
Yet this same woman, raised on a Louisiana sugar plantation, still exudes the graciousness of a Southern hostess whose protected life has surely not encountered difficulties obtaining credit.
IT didn't take long for her to see the need to speak for women in Congress. ''Because you're a woman, you're sensitive to the problems, and you become aware that there's an opportunity,'' she says, taking care not to judge her male colleagues too harshly. ''A lot of the seeming uncaring of male legislators is really that they're unaware. They're not uncaring.'' Mrs. Boggs shows no shyness about the vice-presidency. If picked, she says, she would run ''with vigor.''
''I'm very enthusiastic about a woman for vice-president,'' she says.
''Especially the first vice-president. I think that women have tendency to bring an enthusiasm to a new role and to do it as perfectly as possible because they recognize that they will become the role models in the future.''
Rep. Patricia Schroeder, who despite her relative youth is the dean of the women members of Congress, also holds that having a woman in the No. 2 spot could be a boon for the country. ''Every president says, 'My vice-president is going to be different,' '' says the Colorado Democrat.
''Then they end up plugging the VP into fund raisers and funerals,'' she says , posing the question, ''If you had a woman, would it take away some of the male vs. male competitiveness that always seems to paralyze the office of the vice-presidency?''
Moreover, Mrs. Schroeder scoffs at criticism, especially from liberals, that no qualified Democratic woman exists. ''Would they stand up and say George Bush is not qualified?'' she says, noting that nearly all of the women in the House now have served longer than the four years the vice-president was a congressman. The pool's smaller,'' she says of women qualified for the vice-presidency, but she maintains that they exist.
Mrs. Schroeder, a Harvard-educated lawyer who won her seat on her first try at electoral politics, is generally said to be one in the ''pool.''
She was considered a fluke when elected in 1974. Even Colorado's Women's Political Caucus refused to endorse her at the start because they said it was too soon for her to run for Congress, an irony that she now likes to cite. After her victory, Mrs. Schroeder and her husband confidently picked up their two small children and moved permanently to Washington. Representative Schroeder has steadily entrenched herself in her district as well as become a chief publicist for women's and liberal issues in Congress.
''You're flattered that you're mentioned, but you don't think it's real,'' she says of the vice-presidency talk. She adds, ''It's not a popular idea in Colorado, which already has one candidate (Sen. Gary Hart).''