When Vice-President George Bush's campaign plane landed at Omaha's airport recently, he was greeted by a few dozen cheering Republicans carrying ''Nancy Hoch for Senate'' signs and balloons.
''She is an outstanding candidate,'' the vice-president said, announcing that she was closer than any other GOP woman challenger to unseating a Democratic senator. But Mr. Bush offered no more than a quick endorsement as he climbed into a limousine and drove to a rally in nearby Council Bluffs, Iowa.
Longtime Republican activist and homemaker Hoch faces an uphill battle today. Although President Reagan is running as much as 40 points ahead in Nebraska, she is trailing Sen. James Exon. One Republican who met the Bush plane wore a Hoch sticker, but when asked if she could win, he said, ''I wouldn't touch that one with a 10-foot pole.''
Meanwhile, Minnesota's secretary of state, Joan Growe, is mounting the strongest challenge by a Democratic woman for the Senate, and she, too, is behind.
''The question is whether she can penetrate the cocoon'' of a folksy ''good guy'' image that GOP Sen. Rudy Boschwitz has made for himself, said J. Brian Atwood, executive director of the Democratic Senatorial Campaign Committee.
The two cases symbolize both the progress and the problems for women in politics. In some ways 1984 has been the year of the woman candidate. Democrats put Rep. Geraldine A. Ferraro on the national ticket. Both parties made a publicized push this year to recruit women Senate candidates and to give them maximum legal funding.
Including incumbent Sen. Nancy L. Kassebaum (R) of Kansas, they have nominated 10 women, doubled the previous record in 1980.
But for all these gains, few except those already in office are expected to win.
''This is still what we're trying to overcome,'' Mr. Atwood told reporters recently. ''The women candidates this year are running against very strong Republican incumbents.'' He added that whenever there is a weak incumbent, usually ''a lot of male politicians'' are fighting for the chance to run.
''I think we have to keep trying,'' said Sen. Richard G. Lugar of Indiana, chairman of the National Republican Senatorial Committee. ''Many women simply need higher name recognition.''
Barring a slew of upsets, the House and Senate will retain approximately the same number of women they now have, 2 of 100 members in the upper chamber, and 22 of 435 representatives.
Stephanie Solien of the Women's Campaign Research Fund holds that she is not discouraged by the slow progress. ''The women's political movement is a little more than 10 years old,'' she says. ''What we are trying to do is elect women to 535 of the most powerful seats in the world.''
In a study of women candidates, the campaign research group blames both traditional prejudices and also the reticence of women.
''Women have often waited for party leaders to ask them to run,'' says the recently released study. ''But the reality in politics is that when there is a winnable seat, when there is power at stake, candidates cannot afford to stand back and wait to be asked.''
In the House particularly, the number of women candidates has inched up, from 54 in 1976 to 65 this year. Those who do run usually compete in the most difficult races. As a consequence, the House has only four more women now than 22 years ago.
The Women's Campaign Research Fund discounts one supposed obstacle to women candidates - that women have less success in fund raising than men. By 1982, women and men in similar campaign situations raised approximately equal amounts of money, concludes the group's study.
But the widely held belief that women are shortchanged in donations could discourage some candidates.
At the same time, women have made substantial gains in state offices. Women in state legislatures have increased from 424 in 1973 to 991 in 1983. The number of mayors of cities of 30,000 or more has gone from 12 to 83 since 1973. In statewide races, 19 women are running for office this year, compared with 12 in 1976.
One woman, former Lt. Gov. Madeline Kunin, a Democrat, is running for an open governor's seat in Vermont. Currently, only Kentucky has a female governor, Martha Layne Collins.
Some women have predicted that Representative Ferraro's candidacy for vice-president will help boost other women politicians at all levels. ''Her candidacy has done more for the women's political movement than anything else,'' says Ms. Stolien, partly because from now on ''the public will not find it so unusual'' for a female to run.