Washington — Here's a little quiz for all you political buffs: In the 1978 voting, 63 women were elected as first-time legislators across the United States. Sixty-one of the 63 women belonged to the same political party. Which party was it?
If you answered Democratic . . . well, you were wrong. The correct reply was the Republican Party - you know, the party with the ''gender gap.''
That story illustrates why some Republicans think the whole fuss over the gender gap is a bum rap. After all, they say, just look at the evidence:
Who appointed Sandra Day O'Connor, the first and only woman US Supreme Court justice? President Reagan did.
Which party elected eight out of nine women running for the state Senate in Rhode Island this year? The Republicans.
Who has more women members (three) in his Cabinet than any chief executive in history? President Reagan.
Which party ran several thousand women candidates for state and local offices in 1982, the most women ever offered by the party in one election? The Republicans.
Who recently appointed a woman (Elizabeth Hanford Dole) to head the Department of Transportation, and thereby designated her as the first woman ever to head a US military organization (the Coast Guard)? President Reagan.
All of this seems to make little difference with many women. Despite his recent gains in the polls, President Reagan continues to run about 10 points weaker with women than with men.
The ''gender gap,'' however, is more than just numbers, more than just something dreamed up by pollsters Gallup and Roper.It highlights basic public attitudes toward Reagan and the Republicans which could play a critical role in the 1984 election - and in the future of both the Republican and Democratic Parties.
Behind the gender gap are at least two basic concepts now widely shared.
First is the public view of the ''fairness'' issue - namely, that Reagan and his party have been unfair to the poor (especially to single female heads of households) and unfair to the elderly (the vast majority of whom are women). Reagan & Co. are charged with the ''feminization of poverty,'' with changing federal programs in ways that have hurt women and children the most.
Second is the perception of ''warmongering'' - namely, that Reagan is a saber-rattler who has militarized foreign policy, and who would rather fight than negotiate. Many women ''deeply fear war,'' says Mary Dent Crisp, a former GOP co-chairman. She charges that President Reagan is alienating women with his policies.
Does all of this put a dark cloud over the Republicans in 1984 and beyond?
It could - if that were all that was happening. But Reagan and the Republicans, in the view of a wide range of political experts here, have shrewdly positioned themselves for 1984. Many women have turned away from Reagan. But other women, especially conservative homemakers, have not. And while some groups, such as blacks, have been alienated, others, such as white Southerners, have moved closer to the GOP.
Veteran political analyst Richard M. Scammon says the news media may be putting too much emphasis on the gender gap and thereby missing the big point. In presidential politics, he says, it is the Republicans, not the Democrats, who have become the dominant force.
Look at the record. Despite the Democrats' 2-to-1 advantage in registration, Republicans have clobbered them in presidential elections in 1952, 1956, 1972, and 1980 - plus a narrow GOP victory in 1968. The Democrats won only one landslide - in 1964 - and managed hairs-breadth victories in 1948, 1960, and 1976.
The inside political wisdom in Washington is that Reagan, if he runs, will win again in 1984. Certainly, if recent polls are any indication, the '84 race will be a hard one for the Democrats.
Further, the GOP now dominates the Senate. And in the House, while nostalgia and tradition help to maintain a Democratic majority (largely due to white Southern conservatives voting Democratic), the Republicans have frequently enjoyed an ideological majority, if not a party majority.
Are the Republicans, then, really as bad off as many people suggest? Or are concerns about the ''gender gap,'' the ''black gap,'' the ''Hispanic gap,'' and other gaps overblown?
Analysts say it's a mixed picture. There are genuine concerns. One critic, Republican Sen. Robert Packwood of Oregon, says: ''You cannot write (the women's vote) off and the blacks off and the Hispanics off and the Jews off and assume you are going to build a party on white Anglo-Saxon males over 40. There aren't enough of us left.'' But other Republicans say they have moved to expand that ''Anglo-Saxon base by building support elsewhere. And the President symbolizes that effort.
''Despite what you hear, the John Wayne image hasn't hurt Reagan or the Republicans,'' one analyst suggests. In fact, the image of toughness with the Russians, chopping wood on the ranch, riding horseback, and pumping iron in the White House helps Reagan and the party with groups they need in 1984.
Those groups are the same ones that helped Reagan whip Jimmy Carter in 1980. The most important are:
Men. While Republicans have lost support among women, they have showed impressive strength with the male vote. Men seem to like Reagan's firmness on foreign policy and defense and his efforts to cut waste at home.
Housewives. ''When a woman calls herself a 'housewife' or a 'homemaker' that's almost a political statement, and it probably means she'll vote Republican,'' observes a political strategist. While Republicans have lost ground with career women, housewives support Reagan and the Republicans even more enthusiastically than men.
Labor unions. Despite the Democratic leanings of the leadership, millions of union members swung over to Reagan in 1980, and many are expected to stay with him as the economy gets stronger.
Roman Catholics. The White House has courted Catholics with promises of tuition tax credits for parochial school students, an ambassador for the Vatican (the first in American history), opposition to abortion, and support for school prayer.
Jews. Reagan's tough policy in Lebanon plus his new aid package for Israel plays well with Jewish voters. Supporters of Israel are also concerned about the Mideast policies of some Democratic candidates for president.
Hispanics. Cuban-Americans are firmly Republican, but other Hispanics lean Democratic. Overall Reagan received about 30 percent of the Hispanic vote in 1980, and the latest Gallup poll shows him doing even better, with about 40 percent of the Hispanic vote.
Southerners. Despite major black registration efforts in Dixie, it should be another good year for Reagan. ''You hear lots about black registration in the South. What you don't hear about is the white family of six in the old jalopy voting for the first time. That's been a major new development there,'' one analyst says.
If the Republicans can pull these groups together, Reagan should sweep back into office - though with a somewhat smaller lead than he enjoyed in 1980, political insiders say.
Republicans, of course, would like to have the votes of blacks, career women, and others who lean Democratic. But even getting the black vote up from 10 percent to 20 percent would be a major effort. There's not enough time or money before '84 to do it - and the focus of the campaign has to go where the payoff is big and quick.
''There's an old Tennessee saying,'' says former GOP chairman Bill Brock. ''When you hunt ducks, you go where the ducks are.''
Next: Why the 1988 election is ''the big one.''