There are signs of incipient panic from the White House over the gender gap. First a top White House political operative goes west to tell a gathering of Republican women that the gender gap could "swamp" the Republicans in 1984. Then the White House forms a gender-gap task force to find measures to appeal to women voters. Then this weekend, it comes out with the optimistic analysis that the gender gap has two sides: women may not like President Reagan but men do.

Or as Ann Lewis, political director of the Democratic National Committee, put it: "What they're doing is saying, since we've got ourselves a lemon let's make lemonade."

To set the record straight, President Reagan does, indeed, enjoy greater support among men than among women, but it is neither reliable enough nor numerically substantial enough to offset the losses among women voters he can expect in a reelection bid. According to the polls, his support among men has been hitched to the economy, which means his administration is at the mercy of its economic performance and international variables it cannot always control. If the price of oil goes up between now and 1984, for example, setting off another inflationary spiral, the administration could find its support among men voters jeopardized.

The approval--or disapproval--rating among women, however, has remained relatively constant, giving rise among other things to the interesting question of which sex has trouble making up his mind.

In February 1981, 61 percent of men polled approved of Reagan's performance, while only 52 percent of women did, a nine point difference. In August of that year, a Harris poll showed 65 percent of the men approved while only 49 percent of the women did, a 16 point difference. Just before the November 1982 election, however, a Washington Post/ABC poll showed the gap had narrowed back to nine points, not because Reagan was doing better with women voters, but because his support among men had fallen away: men gave Reagan only a 54 percentage approval rating, compared to 45 percent from women. As of June, the president enjoyed a 60 percent approval rating among men, and only a 47 percentage rating among women.

Women make up 53 percent of the population. In 1980, for the first time, they voted not only in greater numbers than men, but at equal rates. That trend continued in the 1982 election. Given the increased politicization of women as voters, candidates, fund-raisers, campaign managers and so forth, there is every reason to expect them to continue having a greater impact numerically on elections than men.

President Reagan's own polls are showing that younger women, particularly the 6.6 million women who head households, are particularly disenchanted with his policies. The Census Bureau has found that while people 18 to 44 years of age have a lower voting rate than people 45 and older, younger women have a higher voting rate than young men do. In 1980, it was 51.3 percent for young men, and 54.2 percent for young women.

The numbers spell trouble for the administration. Women voters are disenchanted on a number of fronts, ranging from economic policy, which they see as unfair, to foreign policy, which they find bellicose, to concerns about the environment, unemployment, and a host of women's issues, not the least of which is the desire among women to have a say in the affairs of humankind. The current quickening of American involvement in Central America is going to sound a war alarm in their minds. Yet, when President Reagan appointed a 12-member commission on Central America last week, not one member was a woman.

Women voters will be quick to perceive that the current interest at the White House in legislative initiatives to help women has more to do with a commitment to getting President Reagan reelected than a genuine commitment to issues and priorities of women. It is likely to vanish in November 1984 as quickly as it appeared in November 1982, when the women's vote decided elections.

Incumbency is an enormous advantage. For President Reagan, however, it is a distinct disadvantage. He is no longer an unknown quantity. Women voters can look at what he has done for women during the four years he has presided, with one eye on reelection. And they will have to wonder what his administration would do in a second term, when the check of having to face the voters again is gone.