Congressional leaders indicated Tuesday that a compromise is near over how to fund U.S. troops serving in Iraq and Afghanistan after Democrats confirmed they will abandon plans to include a troop withdrawal timetable in the war supplemental spending measure.

House Majority Leader Steny Hoyer pledged that Democrats would try to include a timetable for withdrawal in next year's spending bills.

"We can't pass something without the president's signature and the president can't pass something without our agreement," Hoyer, D-Md., told reporters. "So we can be at a standoff and go back and forth at each other, or we can come to an agreement."

Senate Majority Leader Harry Reid refused to call the compromise a defeat.

"I don't think there's any way you can stretch saying whatever we decided to do in this legislation is a defeat, for heaven's sake, look where we've come. We've come a long, long way," Reid, D-Nev., told reporters on Capitol Hill.

Reid vowed to continue pushing to change the direction of the war in Iraq through the upcoming defense appropriations bill, expecting to vote on the 2008 fiscal year funding measure Thursday night or Friday.

"We’re going to continue our battle — that’s what it is, to represent the American people like they want us to represent them, to change the course in Iraq," Reid said.

Sen. Trent Lott, R-Miss., said Republicans who oppose a timetable will likely get what they wanted.

"We're close to getting a result," Lott said. "We could achieve what we wanted all along and that's to get the funds for the troops without the timelines."

Congressional leaders and White House aides continue to hammer out a compromise after Bush vetoed a $124.2 billion bill on May 1 that would have funded the war through September but demanded that troops begin coming home this fall.

But in a bow to Democrats and some Republicans, the bill will likely include a proposal by Sen. John Warner, R-Va., that would require the president to restrict U.S. aid for Iraq, including reconstruction dollars, if the country doesn't meet benchmarks on political and security reforms.

Warner's proposal would track with recommendations of the Iraq Study Group by requiring two reports on benchmark progress on the Iraq government and consequences if the benchmarks are not met. Warner's proposal also would require the president to comply with withdrawal if the Iraqi Parliament passes a measure to send U.S. forces home.

Warner said his proposal would show America, troops and their families that Congress supports the forces.

Senate Minority Leader Mitch McConnell said Republicans aren't celebrating a victory yet, but expect to pass a bill that would fund the wars for four months without a withdrawal timetable.

“There’s no cheering yet," said McConnell, R-Ky., adding that he hopes to send Bush a bill by Memorial Day.

Sen Robert Menendez, D-N.J., an anti-war critic, said Democrats realize they've reached "a point in time of recognizing the intransigence of this White House on the war." But, he added, "I'm not buying in just because of the threats."

Sen. Russ Feingold, D-Wis., one of the most vocal opponents of the war said he would not go along with the plan and expressed disappointment with his party's leaders.

"I cannot support a bill that contains nothing more than toothless benchmarks and that allows the president to continue what may be the greatest foreign policy blunder in our nation's history. There has been a lot of tough talk from members of Congress about wanting to end this war, but it looks like the desire for political comfort won out over real action," Feingold said.

While a timetable to withdraw troops is out of the bill, a senior House Democratic leadership aide told FOX News that the other issue being worked out is what to do about domestic spending included in the legislation.

Congressional leaders said Monday that the legislation would include the first federal minimum wage increase in more than a decade, a top priority for the Democrats who took control of Congress in January.

A senior administration officials said Bush agreed a long time ago to a minimum wage hike — but the White House wanted significant tax offsets tied to a final minimum wage increase. This official said the bill will include "some offsets" but nowhere near what the White House wanted, a nod to the concessions being made by the president.

Aside from the minimum wage increase being in the bill, "nearly all other nondefense spending" is on the table, with some trimming on the dollar amounts, the House Democratic leadership aide said. White House officials admitted trying to pressure Congress to trim the non-military spending in the final hours — possibly by up to $4 billion of the $20 billion in there — but the war supplemental will have pork.

The House planned to vote Thursday on the bill.

Democratic leaders first will have to sway a large number of Democrats who want to end the war immediately — or pick up enough Republican votes to make up for the losses. Earlier this month, 171 House members voted to order the withdrawal of combat forces from Iraq within nine months.

Rep. Lynn Woolsey, D-Calif., co-founder of the liberal Out of Iraq Caucus, said she will vote against the new measure and predicted that many of colleagues will join her.

"I'm frustrated" with the war, said Rep. Joe Baca, D-Calif., a member of the Blue Dog coalition, a group of conservative Democrats. "But we realize too we have a responsibility to fund our troops and make sure they have the right equipment."

"Every time we negotiate, it (the bill) becomes weaker," said Woolsey, D-Calif. "This is a Republican bill, so it better be Republican votes that pass it."

Hoyer said the next step for his party will be to insist on tougher language in the 2008 military spending bill to be debated this summer.

The final Iraq bill also was expected to insist that U.S. troops meet certain standards before being sent into battle, out of concern from Democrats that some troops were going to Iraq without proper training. But the measure likely would give the president authority to waive this restriction.

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