Madam vice-president, 1984?

THE small plane was bobbing in the gusts of wind blowing up from the Southwest which, for a few hours, had been turning Ohio into a little dust bowl. In a plane en route from Columbus to Cleveland, Gov. Richard Celeste was talking politics. ''I want a woman as our Democratic vice-presidential candidate,'' Mr. Celeste said. ''I think this is the time to do it.''

Celeste had seen a poll that morning which showed that women on the ticket would have little effect - that about the same number of voters who would be attracted by such a slating would find it unpalatable.

But Celeste sees the elevation of a woman to a chance at the vice-presidency as both ''the right thing to do'' and a decided plus for the Democratic Party, ''in the short run as well as the long run.''

Lloyd Bentsen, chairman of the Democrats' Senate campaign committee, was chatting with reporters. He mentioned the ''gender gap'' as being an important factor in what he visualizes as a ''cliffhanger'' victory for the Democratic presidential nominee. ''Women,'' he said, ''will make up about 54 percent of the vote.'' Then he quickly added that he favored a woman in the second spot on the ticket.

''It's a risk,'' said the Texas senator, ''because it has not been tried before. But it's a risk worth taking.''

The Celeste and Bentsen comments reflect a new attitude surfacing within the Democratic Party. When the campaign began last winter, all the Democratic presidential candidates were indicating a ''willingness'' to accept a woman as a running mate. But this often sounded more like the politic thing to say than something these men really wanted to happen or expected to deal with seriously at the convention.

But there is a new wind. As the prospects of a Democratic victory become slimmer, support for a woman on the ticket gains ground. Democratic strategists are not saying so but many are coming around to seeing that their biggest hope is to turn the stream of women support - already running in their direction - into a flood of votes for the Democratic presidential ticket this fall.

One Democratic activist put it this way: ''We need the women to rescue us. And you know they could. So many of them just don't care for Reagan.''

Reagan's pollsters have been working hard to try to find out why the anti-Reagan feeling is so widespread among women. Richard Wirthlin concludes that it stems in large part from what many women perceive as a Reagan belligerency in dealing with the Soviets, which might be leading the United States to war.

But, as the Reagan pollsters will attest, a lot of women don't find Reagan overly attractive as a person. Many describe him as personable but shallow.

So, a shift in Democratic strategy is taking place - from talking about a woman on the ticket to considering it more closely. Thus, it could very well come about.

And who could it be? Governor Celeste says he doesn't have any one woman that he is promoting for the job. He says there are ''many'' who would qualify, reaching from those in Congress down into those in state and local governments. But he did mention a couple of names: New York Congresswoman Geraldine Ferraro and San Francisco Mayor Dianne Feinstein.

Celeste doesn't believe the poll that shows the slating of a woman to be a standoff. He sees the right kind of woman candidate - one who is particularly bright and capable - as a decided plus, someone who would bring women voters to her side and who, at the same time, would attract the male vote.