Before the vote, Democrats argued in vain for minority Republicans to break with Bush and support taking up the measure.
Leon Panetta, chief of staff to Bill Clinton, the former president, said: "To conduct a war, a president needs a unified country, and what this basically tells us is that this country is going to continue to be divided over the war, and it's going to affect his relationship with this congress."
"Has any of the Bush Iraq plans worked other than causing the worst destruction?"
Zaffar Zohair, Islamabad, Pakistan
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Charles Jones, of the Brookings Institution, a US research and policy body, said: "The Democrats are clearly determined to erode (Bush's) credibility, even the legitimacy of decision-making.
"There has been a significant erosion in the postelection-announced comity and now we see that almost anything he does in his capacity as commander in chief is being questioned."
Viviana Hurtado, Al Jazeera's Washington correspondent, said: "As long as the Democrats threaten to curb war spending, the political standoff continues.
"But the president's power of veto means whatever the debate President Bush is likely to get his way, although he could start to lose what little support he has from the American people."
Asked about Democrat attempts to put conditions on the escalation of the war, Tony Snow, the Whitehouse spokesman, said: "To operate under those circumstances is to invite bloodshed on a level that is absolutely appalling, not only in Iraq but possibly in the United States of America ... the president ... is absolutely determined to keep the country safe, that is his job."
The House of Representatives defied Bush on Friday by voting 246 to 182 against the troop increase in what amounted to the first such rebuke since the US-led invasion in March 2003.
The House measure passed with support of virtually all the chamber's 233 Democrats and 17 of its 201 Republicans, many worried about their political fate if they stick with the president on the war.
Polls say most Americans oppose sending more troops to Iraq.
But in the senate, procedural rules allow a minority to block debate and Democrats have a small 51-49 majority.
The upper chamber has been deadlocked on the issue since February 5 when an attempt to bring up a similar resolution opposing the troop increase failed.