WASHINGTON — A Democratic resolution on Iraq has attracted the support of at least two Republicans and is exposing fissures within the Republican Party over the unpopular war.Congressional Republicans are struggling to come up with a united response to President George W. Bush’s plan to send 21,500 more troops to join the estimated 130,000 already there.

Ten Republicans met behind closed doors late Wednesday with Senate Republican Leader Mitch McConnell in a bid to generate consensus on Iraq. The senators emerged from the meeting to announce that no deal had been reached.

“This is a very fluid situation,” said Republican Sen. Jon Kyl.

The meeting came after Sens. Chuck Hagel of Nebraska and Olympia Snowe of Maine, both Republicans who have sparred with the administration on the war, announced that they would co-sponsor the Democrats’ resolution opposing sending more troops to Iraq.

“To feed more American troops into this bloodbath is wrong,” Hagel said Thursday on ABC’s “Good Morning America.” In the end, he said, Iraqis must determine their own future.

In addition to putting the Senate on record against more troops, the resolution calls for the US military mission to switch from major combat to training Iraqi troops, counter-terrorism and keeping foreign fighters out of Iraq.

“It is not in the national interest of the United States to deepen its military involvement in Iraq, particularly by escalating the United States military force presence in Iraq,” the resolution states.

Hagel, a possible presidential contender in 2008 who helped draft the proposal with Democratic Sens. Joe Biden and Carl Levin, called the resolution a “genuine bipartisan effort.”

However, some Republicans denounced it as a political ploy to embarrass Bush. Sen. John Cornyn, a Bush supporter, predicted the resolution would fail.

“If my Democrat colleagues are truly opposed to the mission in Iraq, then as the new majority in Congress they should schedule a serious debate and a vote on cutting off funding for our troops,” said Cornyn, a Republican.

The resolution does not call for a withdrawal of troops or threaten funding of military operations, as many Democrats have suggested. Instead, it says the US should transfer responsibility to the Iraqis “under an appropriately expedited timeline” that is not specified.

Biden, chairman of the Senate Foreign Relations Committee, said his panel will debate the measure on January 24, the day following Bush’s State of the Union address. A swift committee review would pave the way for debate on the floor as early as that week, although Democrats say it is likely Republicans on the committee will want to make changes.

Biden said modest changes to the bill might be used “to attract those who share our view but may not like our specific language.”

Bush sought to stave off a major showdown between the administration and Congress by inviting Republican skeptics of the plan to the White House on Wednesday. But many of those members emerged from the meeting to say they still opposed sending more troops, although they were unsure whether they would back the resolution.

Sen. Norm Coleman of Minnesota, one of several Republicans wary of Bush’s plan, said he is concerned the resolution may go too far. Coleman spokesman Tom Steward said the senator is open to an increase in the Anbar province, for example.