While the Senate's Democratic majority failed to shut off debate on a non-binding resolution that "disagrees" with President Bush's troop surge in Iraq, House Democrats say they think they have a better shot of getting something passed.

Majority Leader Steny Hoyer, D-Md., said Tuesday that House Democratic leaders are drafting their own non-binding resolution on Iraq that signifies opposition to troop escalation.

The resolution is being written by Reps. Ike Skelton, D-Mo., chairman of the House Armed Services Committee, and Tom Lantos, D-Calif., chairman of the Foreign Affairs Committee. Amendments will not be permitted on the resolution, to be debated over three days and wrapped up before the President's Day recess on Feb. 19, Hoyer said.

The House resolution will be based on a Senate model that was pushed back Monday when Republicans deprived Democrats the opportunity to rebuke the White House for President Bush's strategy to add 21,500 troops in Iraq to help end sectarian violence. House Democrats were going to wait for the Senate to act first on a resolution, and decided to go forward after Monday's Senate gridlock.

The vote on a motion to proceed was 49 to 47, well short of the 60 votes necessary to stop discussion and move toward debate of a non-binding resolution sponsored by Sens. John Warner, R- Va., and Carl Levin, D-Mich. Republicans opposed cutting off debate because they wanted votes not only on the Warner-Levin resolution but also on a separate resolution by Sen. John McCain, R-Ariz., supporting the Iraq troop surge and another one by Sen. Judd Gregg, R-N.H., rejecting any future effort to cut off funds for ongoing military operations in Iraq.

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On Tuesday, lawmakers continued to speechify about the failure to debate the Warner-Levin bill, which stated 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."

"Our troops have given so much and they deserve much more than what they got from the United States Senate yesterday. The least we can do is to have this debate and the best we can do is to get this policy right for our troops," said Sen. Amy Klobuchar, D-Minn.

"We ought to, as a Congress, be willing to stand up and say we will be there with the equipment, with the logistics, with the financial support you need to walk those streets as safely as you can possibly do, and that's all this amendment says," Gregg said. "I find it almost incomprehensible that the Democratic leader doesn't want to vote on this language. It is not radical language, it is fairly reasonable language."

Later in the day, Senate Minority Leader Mitch McConnell offered a compromise that would basically eliminate the McCain resolution in favor of the Gregg resolution. But that offer is unlikely to go anywhere since Democratic leaders know that the Gregg resolution could survive the 60-vote filibuster threshold and leave the Senate voting to support the troops and unwilling to cut off funding for the war.

As senators discussed new votes on Bush's policy, two Senate bills unveiled during the day would force the president to move toward a troop withdrawal.

"The only people who believe there is a workable military solution for the conflict in Iraq is the Bush administration," said Sen. John Kerry, D-Mass., in announcing legislation that would require Bush to "complete the redeployment" of American troops within a year.

Sen. Barack Obama of Illinois, a Democratic presidential hopeful, joined two other lawmakers in proposing a measure to block Bush from implementing his planned troop increase and to begin a withdrawal by May 1.

While the Senate debates what to do next, House Democratic Caucus Chairman Rahm Emanuel said movement on the House resolution could start as early as this week with a joint meeting of Skelton' and Lantos' committees to "mark up" the Iraq resolution so the entire House can consider it next week.

"You cannot have an issue like the war with what's happening both on the ground in Iraq and with the request by the president for a record breaking $245 billion for Iraq and not at least have the members of the Congress of both parties have a voice and a vote on whether the escalation is the correct course," Emanuel said.

He added that the joint committee meeting is the first in a series of steps Congress can take in attempts to influence foreign policy and affect the direction in Iraq. One other way is to limit the funding. The budget submitted to Congress by Bush on Monday calls for $624 billion for the Department of Defense, including $141.7 billion for estimated war costs.

Speaking on the budget overall, Rep. John Spratt, D-S.C.., the House Budget Committee chairman, said it's highly doubtful that Democrats could support the administration's budget as is.

FOX News' Major Garrett and Molly Hooper and The Associated Press contributed to this report.