In an effort to push the Senate into passing Iraq withdrawal legislation, the House this week will take up a similar bill that would set deadlines for troop redeployment.

House Democratic leaders made the move as new poll numbers show increasing public dissatisfaction with the war, and as Senate Democrats this week exert pressure on wavering Republicans to pass language in that chamber requiring a troop withdrawal by April 30.

“It will pass here,” a House Democratic leadership aide said, “and hopefully it will give momentum to the Senate.”

However, despite their growing misgivings about the war, most Senate Republicans indicated they would support President Bush’s appeal to wait until September before considering legislation to require troop withdrawals.

While some Republicans have signed on to amendments to the defense authorization bill (HR 1585, S 1547) that would redefine and reduce the military mission in Iraq, only a handful have embraced mandatory timelines.

The House bill (HR 2956), sponsored by Armed Services Committee Chairman Ike Skelton, D-Mo., would require troops to begin withdrawing from Iraq within 120 days of enactment of the legislation. All troops would have to be redeployed from Iraq by April 1, 2008, with minor exceptions.

“The American people want Congress to bring our troops home, refocus our efforts to fighting terrorism and hold the Bush administration accountable,” Speaker Nancy Pelosi, D-Calif., said.

House Democrats will hold a closed-door meeting Wednesday to discuss the bill, but Democratic leaders say they believe the legislation will pass, pointing out that they pushed through similar withdrawal language in the war supplemental in March (HR 1591), which was ultimately watered down in conference.

House Democrats are eager to pass a bill out of Congress that would end the war, lawmakers said after a closed-door meeting late Tuesday. “You have members in the House who understand that the surge has failed,” said Democratic Caucus Vice Chairman John B. Larson, D-Conn.

The bill would allow Bush to keep “minimum force levels” in Iraq to fight terrorism, but he would be required to provide “justification” for that.

Democratic leaders said the House bill language ultimately would be wedded with the withdrawal provision in the Senate. That amendment to the defense authorization bill, by Democratic Sens. Carl Levin of Michigan and Jack Reed of Rhode Island, would require a withdrawal of all but a vestigial U.S. force, to begin in 120 days and end by April 30, 2008.

In the Senate, however, Republican delaying tactics would imperil that amendment and possibly torpedo the entire defense bill. Because the GOP has enough votes to keep Democrats from getting the 60 votes they need to overcome a filibuster, the Republican minority can prevent votes on all the Democrats’ Iraq-related amendments. The parliamentary tactic would buy the White House time until September, when it must report to Congress on the progress of Bush’s surge strategy in Iraq.

Such a GOP strategy could derail the defense bill, which sets military policy, pay raises and funding levels. John McCain of Arizona, ranking Republican on the Senate Armed Services panel, said it appeared “very likely” that the Senate would not pass the bill.

The White House stepped up pressure on the Senate on Tuesday, threatening to veto the defense bill if it requires withdrawal by “an arbitrary date.” Administration officials also lobbied senators to withhold legislation constraining Bush’s options in Iraq until at least September, when General David H. Petraeus, the top commander in Iraq, is to brief Congress on the situation there.

National security adviser Stephen J. Hadley and Lt. Gen. Douglas E. Lute, the administration’s new war czar, have spoken to senators in recent days by telephone and at the White House.

On Tuesday, Secretary of State Condoleezza Rice telephoned lawmakers, including Maine Republicans Susan Collins and Olympia J. Snowe, in an effort to win their support for Bush’s strategy. Vice President Dick Cheney pressed the White House’s case before the Senate GOP’s regular Tuesday policy lunch.

During a visit to Parma, Ohio, Bush dismissed the ideas coming from Congress. He reiterated that troop levels in Iraq “will be decided by our commanders on the ground, not by political figures in Washington, D.C.”

Most Republicans seemed responsive to the administration’s plea for patience.

“September is the time for this debate,” said Sen. Tom Coburn, R-Okla.

With a few exceptions, moderate Republicans who have been critical of the White House are not backing legislation that would set deadlines for withdrawing substantial numbers of U.S. forces

The Levin-Reed amendment is expected to net the support of only a handful of Republicans, potentially including Snowe, Gordon H. Smith of Oregon and Chuck Hagel of Nebraska.

Most other Republicans said they preferred to express their misgivings about the war through legislation that would not include mandatory timelines. They include Richard G. Lugar of Indiana, George V. Voinovich of Ohio and Pete V. Domenici of New Mexico, all of whom publicly repudiated the White House’s position on Iraq in recent weeks.

Collins is working with conservative Democrat Ben Nelson of Nebraska on a proposal that would redefine the mission in Iraq and aim to extract U.S. forces from the country’s sectarian strife.

Another set of Republicans supports an amendment by Lamar Alexander, R-Tenn., and Ken Salazar, D-Colo., that would make the Iraq Study Group’s proposals the policy of the United States, including the group’s recommendation that most U.S. combat troops be brought home by March 2008. Yet, their measure would not require any withdrawals. Six Democrats are cosponsors, plus Republicans Alexander, Collins, Domenici, Robert F. Bennett of Utah and New Hampshire’s Judd Gregg and John E. Sununu.

Meanwhile, in what appeared to be a delaying tactic, Senate Republican leaders insisted on Tuesday that they be allowed to offer alternative measures to the Democrats’ amendments to the defense authorization bill. They also demanded that all the measures meet 60-vote thresholds, whereas Democrats want to have simple majorities.

By insisting on the higher threshold, Republicans effectively ensured that binding Iraq amendments, which do not have that level of support, will not even come to a vote.

In the absence of an agreement, the Senate was scheduled to hold a cloture vote on the first amendment Wednesday. That measure, by Jim Webb, D-Va., would mandate minimum intervals between deployments of active-duty troops and National Guard and Army Reserve forces.

Martin Kady II, Josh Rogin, Bart Jansen and Adam Graham-Silverman contributed to this story.