At issue is a compromise resolution drawn up chiefly by Senator John W. Warner, Republican of Virginia, that says the Senate disagrees with President Bush’s plan to build up troops and calls for American forces to be kept out of sectarian violence in Iraq.

The deadlock came after Democrats refused a proposal by Senator Mitch McConnell of Kentucky, the Republican leader, that would have cleared the way for a floor fight on the Warner resolution in return for votes on two competing Republican alternatives that were more supportive of the president.

One of those alternatives, by Senator Judd Gregg, Republican of New Hampshire, would declare that Congress should not cut off any funds for forces in the field. That vote was seen as problematic for Democrats because many of them opposed any move to curtail spending, raising the prospect that it could have attracted the broadest support in the Senate.

The procedural vote, which divided mostly along party lines, left the Democratic leadership 11 votes short of the 60 needed to begin debate on the bipartisan resolution. Forty-seven Democrats and two Republicans voted to open debate on the resolution; 45 Republicans and one independent were opposed.

The Republicans run a risk with their resistance in the event Democrats are able to persuade the public that Mr. Bush’s allies are stonewalling in the Senate and shielding the president from criticism over an unpopular war. But their show of unity, with war critics including Mr. Warner of Virginia and Senator Chuck Hagel, Republican of Nebraska, siding with the leadership, lent some credibility to Republican claims that Democrats were being unfair. “I am confident that somehow this matter will be worked out,” Mr. Warner said.

But Senator Harry Reid of Nevada, the majority leader, said that “time was tenuous” and that he would not guarantee that Democrats would try again to bring up the resolution. He did promise that there would be more clashes over Iraq policy as the Senate turned to measures like the president’s request for $100 billion in emergency Iraq spending.

“You can run but you can’t hide,” Mr. Reid told his Republican colleagues on the floor. “We are going to debate Iraq.”

The results left the future of the Iraq fight unsettled, though Senate leaders indicated that they would continue to negotiate over ways to restart the debate. Lawmakers on all sides of the issue said they anticipated that the Senate would ultimately approve a resolution of some kind because of intense public interest in the issue. Mr. Reid changed his vote and sided with Republicans at the end, a procedural move to allow him the option to reopen the issue.

Still, as they jousted over the terms of debate, senators provided a taste of what a floor fight over the resolution would look like as they traded tough words about the meaning of a resolution challenging Mr. Bush and what would happen if Congress remained silent.

Senator Joseph I. Lieberman of Connecticut, the independent who sided with Republicans in agreeing not to take up the resolution, called the proposal “a resolution of irresolution,” saying it criticized the president’s plan but did nothing concrete to stop it. He goaded colleagues who opposed the buildup to take more definitive action if that was their view. “Have the courage of your convictions to accept the consequences of your convictions,” he said.

Senator Ben Nelson of Nebraska, a Democratic co-author of the resolution who typically promotes comity in the Senate, accused Republicans of stalling. “If not now, when?” he said. “If not now, do we wait for more troops to die before we oppose the president’s plan?”

In addition to the resolution introduced by Mr. Gregg, declaring that Congress should not cut off financing for forces in Iraq, Republican leaders had sought a Democratic commitment for a vote on another alternative, one introduced by Senator John McCain, Republican of Arizona. That measure would set 11 conditions for the Iraqi government if it wanted to retain American support. The Republican approach would need 60 votes for passage.

Democrats said that the Gregg initiative was meant as a distraction and that they wanted to focus on the question of whether senators supported Mr. Bush’s plan or opposed it. “We are witnessing the spectacle of a White House and Republican senators unwilling even to engage in a debate on a war that claims at least one American life every day and at least $2.5 billion dollars a week,” said Senator Richard J. Durbin of Illinois, the No. 2 Democrat.

Some Republicans admitted that they were unsure how long the unity would last and whether Republicans could continue to make a case against the resolution on procedural grounds. And two Republicans facing re-election in 2008, Senators Susan Collins of Maine and Norm Coleman of Minnesota, joined Democrats in voting to begin the debate.

Democrats tried to immediately pounce on the vote, with Mr. Reid saying Republicans had given Mr. Bush the green light to begin his buildup. They also warned of political consequences for Republicans given public frustration with the war.

“Senator McConnell led his Republican troops off the cliff,” said Senator Charles E. Schumer of New York, chairman of the Democratic Senatorial Campaign Committee.

The White House welcomed the Senate vote. “All sides have a right to be heard in this debate, and we support Senator McConnell’s and the Republicans’ right to be able to offer the amendments they want to offer,” said a spokeswoman, Dana Perino.

Senator John Sununu, a Republican of New Hampshire who is also up for re-election next year, acknowledged that voters were likely to be unhappy with the procedural wrangling over an issue as grave as Iraq.

Mr. Sununu, who sided with Republicans, but declined to say whether he would ultimately vote to oppose the Iraq plan, said, “It may come as a surprise to my colleagues, but most voting members of the American public think that the Senate spends all too much time talking and not enough time casting votes.”