The House Democratic Caucus voted Thursday to try to block the tax-cut deal that President Obama struck with Republicans, a move that does not kill the legislation but shows that its opponents are digging in.

Rank-and-file Democrats passed a nonbinding resolution, introduced by Rep. Peter A. DeFazio (D-Ore.), by voice vote that said the tax package should not come to the House floor for consideration.

And in her first explicit declaration of dissatisfaction since the tax deal was cut, House Speaker Nancy Pelosi (D-Calif.) suggested that she would not bring the package to the floor in its current form.

"House Democrats share the president's commitment to providing the middle class with a tax cut to grow the economy and create jobs" but "reject the Senate Republican tax provisions as currently written," Pelosi said. "We will continue discussions with the president and our Democratic and Republican colleagues in the days ahead to improve the proposal before it comes to the House floor for a vote."

After the caucus vote, House Majority Whip James E. Clyburn (D-S.C.) said: "People would like to see every opportunity to make revisions, and I'm one of them." Asked whether he still expected the tax deal to come to the House floor for a vote, Clyburn said, "I don't make those decisions."

Said Rep. Lloyd Doggett (D-Tex.): "If it's take it or leave it, we'll leave it."

At one point during the meeting on the vote, House Democrats erupted in a chant of "Just say no!"

The White House played down the drama.

"If there are ways to strengthen the framework that are agreeable to everybody and strengthen the coalition, that's good," White House press secretary Robert Gibbs told reporters at his daily news briefing.

Gibbs predicted that "at the end of the day, Congress will give the American people a vote on a plan that prevents their taxes from going up by several thousand dollars at the beginning of the year, that will prevent millions from losing their unemployment insurance, and, as this agreement does . . . give strong incentives for job creation and economic growth."

Members of Congress "are not going to want to be in their districts, senators are not going to want to be in their districts, when their constituents find out on the first of January that their taxes have gone up by several thousand dollars," Gibbs said.

Even as House Democrats expressed their unhappiness, however, larger forces were rallying around the tax deal. Thursday afternoon, the White House released a letter from the United Auto Workers, a labor group influential in Democratic policies, announcing its support for the package.