The vote was 56-34. That was four short of the 60 needed to advance the measure, which is identical to a nonbinding resolution that Democrats pushed through the House on Friday.
"The Senate, on behalf of the American people, must make it clear to the commander in chief that he no longer has a rubber stamp in Iraq," said Majority Leader Harry Reid, D-Nev., in the final moments before the vote.
Republicans blasted him and the Democratic leadership for refusing to allow a vote on an alternative that ruled out any reduction in money for troops in the field.
"A vote in support of the troops that is silent on the question of funds is an attempt to have it both ways," said Sen. Mitch McConnell of Kentucky, the GOP leader. "So we are asking for an honest and open debate."
The vote marked the second time this winter that Senate Republicans have blocked action on nonbinding measures critical of the president's war policies. This time, however, there were signs of restlessness within the GOP.
Seven Republicans broke with their leadership, compared with only two on the previous test vote.
Also this time, the maneuvering concerned a nonbinding measure that disapproved of Bush's decision to deploy the additional troops and pledged to support and protect the troops.
The vote in the House on Friday was 246-182, with 17 Republicans breaking ranks to support the measure and two Democrats voting in opposition.
Saturday's debate and vote occurred in an intensely political environment, both in and out of the Capitol.
It sent some members scurrying back to Washington, D.C., from what was to have been a long holiday weekend, reports CBS News correspondent Joie Chen. Some presidential wannabees bailed out of big campaign appearances. Because although nobody thought the measure had a chance of passing, most senators couldn't risk the political backlash they'd face for not showing up.
One of them, Democratic Sen. Hillary Rodham Clinton of New York, squeezed in a morning appearance in New Hampshire, where she told one audience, "We have to end this war and we can't do it without Republican votes."
Polls show strong public opposition to the war, which as killed more than 3,100 U.S. troops. Democrats seemed eager to force Republicans into votes that might prove politically troublesome.
"They are torn between their president's policy and the wishes of the constituents, but vote they must," said Sen. Charles Schumer of New York, head of the Senate Democrats' campaign committee.
Democrats in both the House and Senate have said the nonbinding measures would be only the first attempt to force a shift in Bush's war policies.
In the Senate, Reid has told lawmakers he will turn anti-terrorism legislation into a forum for debate over the war. He has met privately in recent days with fellow Democrats as the leadership plans its next move.
In the House, Democrats have said they will attempt to place restrictions on Bush's request for an additional $93 billion for the military in an attempt to make it impossible for him to deploy all 21,500 additional troops.
Rep. John Murtha, D-Pa., has described a series of provisions that would require the Pentagon to meet certain standards for training and equipping the troops, and for making sure they have enough time at home between deployments.
Murtha and House Speaker Nancy Pelosi, D-Calif., describe these provisions as designed to protect the troops.
Republicans argue the effect would be to deny troops needed reinforcements and are expected to try to block the restrictions.