The Democrats emerged from the midterm elections buoyed about their chances of capturing the White House, but still divided over whether 1990 produced the formula that will get them there.

Many Democrats argued yesterday that this year's elections had liberated their party from the doldrums of the Reagan era because the budget debate had finally allowed them to talk about the economy in a way that put the Republicans on the defensive as the party of the wealthy.

But with several governors -- of both parties -- tossed from office yesterday by voters angry about taxes, government ineptitude and recession, other Democrats cautioned that the party needed far more than a "tax the rich" banner. They noted that the Democrats narrowly lost governorships in California and in three critical midwestern states -- Illinois, Ohio and Michigan -- where taxes, the economy and the budget were crucial issues.

Racially charged contests in North Carolina and Alabama, both won by Republicans, also reminded Democrats that they have not yet escaped the quagmire of social and racial issues left over from the 1960s.

Democrats were gleeful about the failure of President Bush's campaigning to produce more victories for his party. "We are going to insist that in 1992, George Bush campaign in all 50 states to ensure that a Democrat be in the White House," said Ronald H. Brown, the Democratic national chairman, who pointed particularly to Democratic gubernatorial triumphs in the Bush strongholds of Florida and Texas.

Brown's comments reflected a virtually unanimous view among Democrats that Bush is clearly vulnerable. After almost two years in which Democrats appeared to be running away from challenging the president in 1992, they said, the prospect of beating him would concentrate the minds of many potential challengers.

"I think we'll see an immediate resurgence of Democratic presidential politics," said Texas pollster George Shipley. Among potential candidates who enjoyed strong showings Tuesday were Sens. Albert Gore Jr. (D-Tenn.) and Sam Nunn (D-Ga.), whose political strength at home was demonstrated by the fact that he ran unopposed, and Gov. Bill Clinton (D-Ark.). Other prospects include Jesse L. Jackson, who won overwhelmingly Tuesday for the post of shadow senator in the District, House Majority Leader Richard A. Gephardt (D-Mo.), Sen. Lloyd Bentsen (D-Tex.) and Gov. L. Douglas Wilder (D-Va.).

But two of the Democrats' most promising national prospects performed far below expectations Tuesday. In New Jersey, where voters are mutinous over tax increases pushed through by Democratic Gov. Jim Florio, Sen. Bill Bradley barely survived a challenge from a little-known, barely financed Republican, Christine Todd Whitman. Exit polling showed that Bradley was badly hurt by the tax revolt.

In New York, where taxes have gone up and the state economy has thrown the budget into deficit, Gov. Mario M. Cuomo, who coasted to victory with 65 percent four years ago, was held to 53 percent in a multi-candidate field.

"How do people explain how Bill Bradley and Mario Cuomo, two supposed superstars in the party, are barely able to get 50 percent of the vote?" said Paul Maslin, a Democratic pollster, who cautioned against too much Democratic crowing.

There was certainly a lot of that yesterday from party leaders who celebrated the turn the tax debate had taken. After a decade of being accused of wanting to raise everyone's taxes, the Democrats -- thanks to Bush's handling of the budget talks -- could talk about protecting the middle class by taxing the rich.

"I think the message for Democrats is that the Republican formula used by Ronald Reagan has collided with reality and the voters are no longer buying it," said Gore.

"At the very least, there is a feeling of self-confidence that was nonexistent as recently as nine months ago," said Geoff Garin, a Democratic pollster. "Democrats have moved the debate back onto turf where they're more competitive and have more to offer."

Robert Borosage of the Institute for Policy Studies said "pent-up demand for change" helped elect such progressives as Paul Wellstone, who shocked Sen. Rudy Boschwitz (R-Minn.), and Bernard Sanders, a socialist elected to the House from Vermont.

But Garin warned the Democrats not to sit on their successes. "There has to be some sense of an economic policy that is more than just redistributing the burdens of taxation," he said. "My guess is that 1992 will be much more about getting the country's economy moving again. The answer has to be something more than just fairness."

If there is a central Democratic worry, it is that the tax-the-rich theme, handled poorly, could backfire and recast the Democrats simply as the party of taxes. "The truth of economic populism is not just tax the rich," said Mandy Grunwald, a Democratic strategist. "It's also about giving the middle class a break -- it's the second part of the message. Too much emphasis was put on the first part, so what you end up with is a tax message and not an economic message."

Few offered a more compelling cautionary tale for Democrats than Bradley, who still sounded shaken by the voter backlash he ran into. "What I encountered was a level of frustration, anger and fear that emanates from the incredible financial pressures" that most families feel.

He added: "You've got to have something positive to say to families under stress."

Such pressure was especially strong against incumbent governors who raised taxes, which gave some Democrats pause. "At a time when people lack confidence in government and are worried about the economy, they're not anxious to pay additional taxes," said Thomas E. Donilon, a Democratic strategist.

Democrats faced another problem: voters' hostility to government, which hurts a party whose historic task has been to use government to achieve social and economic ends.

"The role of government is one of the central subjects Democrats have to address," said Gore. "When people are helped by government, how are they helped? What are the results? And what obligations are imposed on those who receive the help to do their part in ensuring a successful outcome?"

The debate over whom the government should help puts the Democrats face-to-face with their most sensitive problem: race.

The Republicans used overt racial appeals to win the North Carolina Senate race, where Sen. Jesse Helms defeated black Democrat Harvey Gantt, and the Alabama governorship, where incumbent Gov. Guy Hunt defeated Democrat Paul Hubbert.

And in the California governor's race, perhaps the biggest prize of 1990, Sen. Pete Wilson put Democrat Dianne Feinstein on the defensive by saying she would impose racial quotas on state hiring. Wilson won a very narrow victory.

The issue will be kept alive in the next Congress as Democrats try again to pass a civil rights bill similar to the one Bush vetoed last month, saying it would impose quotas in hiring. Ronald Walters, a professor of political science at Howard University, said the addition of one Democratic senator could be enough to override a Bush veto next year. But he warned that in 1992, "Republicans will have a big stick in affirmative action to wave at Democrats."

Stuart Eizenstat, who was President Carter's chief domestic policy adviser, said that because "the Republicans have lost two key issues of anticommunism and taxes, this quota and affirmative action issue is going to be a vital theme."

Garin said that in Louisiana, where Republican David Duke, a former Ku Klux Klan leader won 60 percent of the white vote in an unsuccessful U.S. Senate race last month, young whites often complained that Democrats were "elitists" who seemed to care more about the environment or poor people than about the economic aspirations of whites with modest incomes.

"Democratic positions on race issues would be a lot less scary if those {white} voters were convinced the Democrats were looking out for their economic well-being," Garin said.

And there is another side to cultural liberalism that could actually help the Democrats, said former House Democratic whip Tony Coelho. Future rulings of conservative judges appointed by former president Ronald Reagan on abortion and other "lifestyle issues," he said, could push many younger voters toward the Democratic Party.

"We've got to be patient," he said. "The pendulum is swinging back."

Staff writer David S. Broder contributed to this report.