The No. 2 Democrat in the Senate said Thursday the debate over non-binding resolutions on Iraq is over, and Democrats are now looking at a bill proposed by Sen. Ted Kennedy that would cut funding for President Bush's troop surge proposal.

"We're moving to stage two — much more extensive, direct action," said Senate Majority Whip Dick Durbin of Illinois, adding that it's now time to move to binding legislation.

An aide to Senate Majority Leader Harry Reid said Democrats are moving in the direction of a more substantive debate on Iraq and legislation with teeth. Reid said he is now taking counsel on Iraq from Kennedy.

"He's the quarterback," Reid said, joking that Kennedy, D-Mass., is one of the only senators not running for president with a plan for Iraq.

The aide told FOX News that Reid is not suggesting that Kennedy's Iraq bill will be the subject of debate, but it points to the desire of many within the Democratic Caucus to do more. The aide added that Reid hasn't ruled out a resolution altogether and that in the weeks ahead, the Senate might still take one more crack at a non-binding expression from the Senate.

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Under Kennedy's bill, Bush would be required to seek a separate authorization from Congress approving his recent decision to increase the number of troops in Iraq by 21,500. If he didn't get that authorization, Congress would refuse to give funding for the Pentagon to institute the new plan.

Kennedy aides are quick to note that the funding cut would not touch any troops who are currently in Iraq. The military has already begun sending some of the 21,500 troops into Iraq.

Kennedy's bill so far has several Democratic co-sponsors, including Sens. John Kerry of Massachusetts, Robert Menendez of New Jersey, Tom Harkin of Iowa, Patrick Leahy of Vermont, Chris Dodd of Connecticut and independent Bernie Sanders of Vermont. It currently has no Republican co-sponsors.

Kennedy, who introduced his bill on the eve of the president's Jan. 10 announcement on the new plan, has long been an advocate for bringing troops home from Iraq, which he says is in the middle of a civil war. In January 2005, he began calling for the troop withdrawal and drawing parallels between Iraq and the Vietnam war.

Even with talk of moving Kennedy's bill, several lawmakers are still hoping for a non-binding "Sense of the Senate" resolution.

Republican Sens. John Warner of Virginia, Chuck Hagel of Nebraska and five others wrote Reid on Wednesday saying they want a vote on the resolution authored by Warner and Sen. Carl Levin, D-Mich., that expresses disapproval of Bush's plan to send that many more troops to help secure Baghdad.

On Monday, Senate Republicans minus Sens. Norm Coleman of Minnesota and Susan Collins of Maine voted to oppose bringing the resolution to a vote to protest Democratic leaders who would not allow two other resolutions supporting benchmarks in Iraq and continued funding for U.S. forces.

"We strongly believe the Senate should be allowed to work its will on our resolution as well as the concepts brought forward by other senators. Monday's procedural vote should not be interpreted as any lessening of our resolve to go forward advocating" the resolution, reads the letter signed by those four Republicans, as well as Sens. Olympia Snowe of Maine, Gordon Smith of Oregon and George Voinovich of Ohio.

"We will explore all of our options under the Senate procedures and practices to ensure a full and open debate on the Senate floor. The current stalemate is unacceptable to us and to the people of this country," the letter continues.

Reid spokesman Jim Manley told FOX News that Reid will try to block efforts to attach the resolution to other legislation.

"Senator Reid gave Senator Warner and the others a chance to vote for their own resolution on Monday, but only two of them chose to do so," Manley said. "Hopefully this letter signifies that the others have had a change of heart, and will be willing to vote for their own resolution in the future."

Senate Democrats believe Republicans have begun to squirm under the political pressure of appearing to duck a debate on the anti-surge resolution. Republicans admit they are losing the battle of the headlines and airwaves, but have shown a degree of resilience that's surprised Democratic leaders.

Asked about the letter, White House press secretary Tony Snow said Republicans never opposed a debate on the Iraq resolutions, but wanted to have a full vetting of all the resolutions. He said misimpressions had been left that Republicans were blocking the measure, when in fact, their complaint was they were not permitted a full and open debate.

Reid's refusal to allow a vote could intensify pressure on the GOP to relent on the other options.

Republicans know they don't have even 50 votes in support of the troop surge. For that reason, they wanted to focus instead on the resolution offered by Sen. Judd Gregg, R-N.H., that deals with future Iraq war funding — an issue that divides Democrats more than Republicans.

Gregg's alternative says Congress should not take "any action that will endanger United States military forces in the field, including the elimination or reduction of funds for troops in the field, as such an action with respect to funding would undermine their safety or harm their effectiveness in pursuing their assigned missions."

Meanwhile, House Democratic leaders said Thursday they are scheduling three days next week to debate a new resolution that expresses disagreement with the troop increase.

"The entire effort here is this will be and is a vote on whether you support or don't support the escalation as enunciated by the president," said Democratic Caucus Chairman Rahm Emanuel, D-Ill. "To make it anything else was to get off of what is the debate we've had in this country, not just the Congress, in this country on whether this was the right policy as enunciated."

House Majority Leader Steny Hoyer of Maryland said Democrats are not going to abdicate their responsibility in determining the best course of action in the overall War on Terror.

"We have had some 22 hearings already in the four weeks this year in the various committees dealing with various aspects. ... We, Democrats, are absolutely committed to the war on terrorism, to protecting the American people and protecting our country. We do intend to play a significant role ... in determining how best to confront and how best defeat terrorism," Hoyer said.

Reid and Durbin said it is possible the Senate could take up the House-passed resolution by the end of February when Congress returns from its President's Day recess. No language is yet available on that measure, but Durbin said what he is "hearing from the House is that it will be binding."

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