WASHINGTON – In another sign of Republican unease with the president’s Iraq policies, a third GOP senator expressed support Thursday for pulling U.S. forces out of Iraq under certain conditions.

Sen. Olympia Snowe announced she would sponsor a bill to require American commanders to plan a withdrawal within 120 days of the bill’s enactment, unless the Iraqi government meets a series of benchmarks.

“The Iraq government needs to understand that our commitment is not infinite,” said Snowe, a moderate from Maine who frequently departs from the party line.

President Bush has insisted that Congress not impose any limits on his conduct of the four-year-old war. But Snowe, who voted earlier this year to oppose the president’s troop buildup, has taken issue with that view. “It is our business as well,” she insisted Thursday.

Snowe is not backing a Senate Democratic plan approved last month that would require the president to begin withdrawing troops within 120 days and would set a nonbinding “goal” of completing the withdrawal by next March. But that plan did draw the support of two GOP senators, Chuck Hagel of Nebraska and Gordon H. Smith of Oregon.

The Senate proposal and a House version approved last month – which both include benchmarks for the Iraqi government to meet – are being merged into one proposal. Democratic leaders said they expect to have the compromise measure ready for a vote next week.

Bush, who has promised to veto the measure and has spoken out forcefully against it, took his campaign on the road Thursday at a town hall event in House Minority Leader John Boehner’s western Ohio district.

Snowe’s legislation marks another challenge to a White House that has worked to keep GOP lawmakers on Capitol Hill from backing any congressionally mandated limits on the president’s war powers.

The effort has thus far been very successful.

Only two GOP lawmakers in the House and two in the Senate crossed the aisle last month to vote for the Democratic withdrawal plans.

And congressional Republicans have repeatedly reiterated their support for the president in recent weeks, traveling to the White House to stand with the chief executive.

At the Capitol, Senate Minority Whip Trent Lott, R-Miss., dismissed the effect of Snowe’s decision to challenge the president’s leadership.

“It doesn’t matter. … We’ve got plenty of votes,” said Lott, whose 49-member caucus could sustain more than a dozen defections and still prevent Democrats from overriding a presidential veto.

Republican leaders Thursday focused their attacks on Senate Majority Leader Harry Reid, D-Nev., who said at a news conference that he believes “the war is lost.”

“I can’t begin to imagine how our troops in the field, who are risking their lives every day, are going to react when they get back to base and hear that the Democrat leader of the United States Senate has declared the war is lost,” said Senate Minority Leader Mitch McConnell, R-Ky.

But Republicans continue to face greater challenges keeping their members on the same side as the president as public impatience with the violence in Iraq continues to mount.

McConnell refused last week to say when he thought Americans would know whether Bush’s surge has succeeded. But some Republicans who voted with the White House last month are saying privately that the president has only a few more months to demonstrate success.

In her proposed legislation, which does not yet have any cosponsors, Snowe put her own limit at just four months.

Under her bill, if the Iraqi government has not met the benchmarks – which include disarming militias, amending the constitution and passing legislation to equitably share energy resources – the U.S. commander in Iraq must submit a plan for withdrawing U.S. forces.