A day after House lawmakers failed to override President Bush's veto of a war spending bill that demanded U.S. troops begin withdrawing from Iraq by this fall, the top Senate Democrat said "nothing is off the table" in a compromise bill

Following discussions with the White House, Senate Harry Reid told reporters that he has not abandoned any plans that insist on a troop pullout.

"There is nothing off the table -- including timetables, benchmarks, waivers from the president, waivers from the secretary of defense. ... Nothing," Reid said.

Reid spoke after Bush's top deputy, White House Chief of Staff Josh Bolten, met on Capitol Hill with the Democratic leader and Senate Minority Leader Mitch McConnell, R-Ky., as part of in efforts to get a new bill to the president's desk by Memorial Day.

Lawmakers said they are ready to work with the White House, but signaled no deal is near. The House failed Wednesday to gain a two-thirds majority to override Bush's veto to a $124.2 billion bill ordering troops to begin coming home by Oct. 1.

After a 45-minute meeting with Bolten, Reid said, "No one wants out of Iraq more than I do," but acknowledged that Democrats don't have enough support to force a withdrawal from Iraq.

"Do I want one? Yes, but I don't think we can get it done," Reid said.

Bolten offered proposals for a compromise, making it clear he was coming "with the authority from the president to negotiate," Reid said.

Other Democrats hinted that they couldn't get a timetable for withdrawal past the White House, but they should at least insist that Iraqis live up to their end of the deal to secure their country.

"If we're not going to hold the overall administration accountable, let's at least hold the Iraqis accountable," said Sen. Dick Durbin, D-Ill.

McConnell gave no indication about reaching a deal, but said they plan to meet again next week.

Bolten and budget director Rob Portman also met with Reps. David Obey, D-Wis., and Jerry Lewis, R-Calif.

Democrats had indicated that they might back off their previous demand to begin withdrawing troops, but want influence on war policy through benchmarks set for the Iraqis to achieve such as disarming militias, reconciling Sunnis and Shiites, sharing oil resources and spending its own money on reconstruction efforts.

"The goal is obviously to strengthen our military, to support our troops, to honor our promises to our veterans, to hold the Iraqis accountable so that we can end this war, to bring stability to the region, to turn our attention to the War on Terror," House Speaker Nancy Pelosi said after meeting with Bush at the White House shortly after the failed House vote.

Democrats say setting a timeline for U.S. troop withdrawals is necessary to provide the accountability that's been missing from the war. One proposal would call for some U.S. troops to leave violent regions of Iraq, such as Baghdad, and move to less-violent areas of Iraq if benchmarks are not reached.

"Benchmarks are important, but they have to have teeth in order to be effective," Pelosi said.

Administration officials and congressional allies argue the Iraqis shouldn't be punished with a withdrawal of financial or military support.

"I am confident that with goodwill on both sides that we can move beyond political statements and agree on a bill that gives our troops the funds and flexibility to do the job that we asked them to do," he said in a speech in Washington before The Associated General Contractors of America.

House Minority Leader John Boehner told reporters he was optimistic that Congress would reach a compromise without setting a timetable for withdrawal.

“Artificial timetables will never be acceptable to my Republican colleagues,” Boehner said Thursday on Capitol Hill. “There’s a large majority in the House and Senate opposed to surrender dates."

Summer Vacation

Congress isn't agreeing how to fund troops yet, but lawmakers do have one thing in common: they're not happy that Iraqi politicians might take a long vacation this summer.

"If they go off on vacation for two months while our troops fight — that would be the outrage of outrages," said Rep. Chris Shays, R-Conn.

The Iraq parliament's recess, starting this July, would likely come without Baghdad politicians reaching agreements considered key to easing sectarian tensions. Examples include regulating distribution of the country's oil wealth and reversing measures that have excluded many Sunnis from jobs and government positions because of Baath party membership.

"That is not acceptable," Sen. John Warner, R-Va., said of a two-month recess. "An action of that consequence would send a very bad signal to the world that they don't have the resolve that matches the resolve of the brave troops that are fighting in the battle today."

FOX News' Wendell Goler, Trish Turner and The Associated Press contributed to this report.