Some Republican leaders on Capitol Hill Monday offered a new resolution disapproving President Bush's plan for a troop surge in Iraq, but one they say is less confrontational than a draft proposal being circulated among Democrats.

The GOP measure is sponsored by, among others, Sen. John Warner, R-Va., ranking Republican on the Senate Armed Services Committee, and a lawmaker once solidly in the president's corner.

"The purpose is not to cut the forces to current levels or to set any timetables for withdrawal, but rather express genuine, and I repeat the genuine concerns, of a number of senators from both parties about the president's plan," Warner said.

Meanwhile, in the House, Minority Leader John Boehner sent a letter to House Speaker Nancy Pelosi asking for her support in a plan to build a new committee that would have the sole purpose of oversight in Iraq.

"The new majority has two choices," Boehner said in a press conference. "They can either try to stop the president's new strategy and block funding for our troops or they can join us in aggressively holding the Bush administration and Iraqi government accountable for achieving success."

In his letter to Pelosi, he said that the existing committee system responsible for Iraq policy in the House — primarily the House Armed Services, Foreign Relations and Appropriations committees — is too disparate to focus exclusively on the issue at hand.

"A select panel, by contrast, will afford the House of Representatives an opportunity to bring together members with expertise to provide oversight and thoughtful analysis of the progress being made under the new strategy" offered by Bush, Boehner wrote.

Boehner warned against other measures that would attempt to have the United States vacate Iraq within the coming months.

"An arbitrary withdrawal of our troops at this time would constitute a direct threat to the safety of the American people. The president has determined our troops in harm's way are in need of reinforcements, and their deployment has already started," Boehner wrote.

The dissipation of rock-solid support in the president's plan comes one day before he is to deliver his sixth State of the Union address. The speech is expected to reinforce Bush's Jan. 10 announcement ordering an additional 21,500 U.S. troops to Iraq to try to settle the sectarian violence and give the country's government another chance to take over its own security.

Watch President Bush's State of the Union address on streaming video live on FOX News.com Tuesday night at 9 p.m. EST.

The plan drew a critical response from Democrats, but some Republicans have also joined in, saying they are concerned about the fallout of failure in Iraq, which would not be the president's but that of the Iraqi government.

In the letter to Pelosi, Boehner, R-Ohio, suggested that "benchmarks" be listed to measure Iraqi progress and the administration response should the Iraqis fail to meet those goals. Under the benchmarks, the president would be required to sign off on steps being made in the country and report to Congress monthly.

"As you know, Congress cannot and must not dictate the strategies or methods used in war, but we have a duty to the American people to candidly and honestly assess whether our efforts have been successful," the letter reads.

Throwing support behind the GOP leader, House Minority Whip Roy Blunt of Missouri issued a statement saying lawmakers should give Boehner's proposal a chance.

"Before anyone in the House moves to disavow the war or cut funding for the president's policy in Iraq, we propose that Congress exercise its important constitutional responsibility for oversight of the plan."

Pelosi's office did not have an immediate response.

In the Senate, Warner was flanked by fellow Republicans Susan Collins and Norm Coleman as well as Democratic Sen. Ben Nelson to unveil a resolution designed to be a more moderate rebuke of the president's plan than one being sponsored by Democratic Sens. Joe Bidden of Delaware and Carl Levin of Michigan and Republican Sen. Chuck Hagel of Nebraska

Warner — who last month said he believed that Iraq was "drifting sideways" — said his resolution keeps in mind the safety of the U.S. military in Iraq, respects the president's constitutional authority and reminds him to consider all the options available to him.

"I personally, speaking for myself, have great concern about the American G.I. being thrust into that situation [in Iraq], the origins of which sometimes go back over a thousand years, and trying to sort out — with the difficulty of language, with the difficulty of understanding the culture — how best to react to Sunni upon Shia, Shia upon Shia, Sunni upon Sunni and other things," Warner said.

The resolution would not have the full weight of law, but would express that "the Senate disagrees with the plan to augment our forces by 21,500, and urges the president instead to consider all options and alternatives for achieving the strategic goals ... with reduced force levels than proposed."

The resolution also says the objective in Iraq should be to encourage Iraqi leaders to foster political reconciliation among ethnic groups and allow the military to maintain "territorial integrity of Iraq" and prevent terrorists from getting a foothold in the country.

Warner said that the resolution is not meant to be a rival bill to the Biden-Hagel-Levin plan, and said he would wait to see how the rival proposal evolves once it is introduced Wednesday.

The Biden-Hagel-Levin resolution's primary language says "it is not in the national interest of the United States to deepen its military involvement in Iraq, particularly by escalating U.S. troop presence in Iraq."

If the Biden-Hagel-Levin resolution doesn't change form, however, Warner said he would offer his resolution as a substitution. Other senators hedged, saying they'd wait and see what was reported from the Senate Foreign Relation Committee.

Wrapping up their press conference, the senators dodged questions about how much support they thought the latest resolution would garner.

"Who knows?" Collins said.

FOX News' Major Garrett and Gregory Simmons and The Associated Press contributed to this report.