Democrats are not done trying to stamp out Iraq war policy, Senate Majority Leader Harry Reid said Monday, announcing two more votes to be taken on the matter this week as the Senate attempts to pass a controversial war spending bill.

Debate is scheduled to start on new legislation on Thursday. The first measure would call for troops to begin leaving Iraq by Oct. 1 with a final deadline of April 1, 2008, except for only a small fraction of current forces. The $120 billion bill would provide money for both military operations in Iraq and Afghanistan, as well as domestic projects. That's nearly the same measure that President Bush vetoed once already.

The second measure would cut off funding for combat after March 31, 2008.

Neither measure is expected to pass, but the move comes as Republican support for the war would appear to be cracking under pressure. Last week, 11 moderate House Republicans met with the president, telling him that their support for the war can't hold out forever in the face of dwindling public support for the war and upcoming elections.

Despite one presidential veto on the books, the House last week passed another version of the war spending bill: a two-part, $95 billion bill that would disburse the money in installments and would require a second vote for the second installment. The Senate has been cool to that plan.

The measures announced Monday would give anti-war critics their first chance to vote to cut off war funds, and would serve to gauge GOP support for some kind of timeline in the war spending bill.

The votes would be on amendments tied to an unrelated water resources bill currently on the Senate floor. The first vote could come as early as Tuesday.

That vote is basically a reconstituted version of a bill offered up by Reid and fellow Democrat, Senate Armed Services Committee Chairman Carl Levin. Their original bill — which had a redeployment goal of April 1, 2008 — made it out of the Senate but later failed as part of the overall spending bill.

The new language to be included in the amendment would add a waiver clause, possibly drawing Republicans who want to send a strong message on the war while not setting any mandatory withdrawal dates, a move some call "micromanaging the war."

But passage of the $120 billion in war spending would not allow the Senate to begin negotiating with the House and send President Bush a bill by the end of the month, said Rodell Mollineau, a Reid spokesman. Nevertheless, he added, "these are important votes. This will give members an opportunity to debate these issues and have up-or-down votes on these."

Levin said the new version "would build upon the provisions in the vetoed bill by providing consequences for the government of Iraq's failure to make substantial progress towards meeting the political benchmarks that they had agreed upon among themselves."

He added that "by providing for the presidential waiver, we are removing any reason for the president to veto the supplemental funding bill."

The second amendment will be on legislation sponsored by Reid and Sen. Russ Feingold, which would stop spending for the war by April 1, 2008, with the exception of a limited mission including counterterrorism, force protection and Iraqi troop training.

A senior Senate Republican leadership aide told FOX News that Republican alternative amendments are possible as well.

Feingold said he was pleased with the news of the upcoming debate.

"The American people deserve to have the Senate go on record about whether or not it wants to end our misguided mission in Iraq and safely redeploy our brave troops," Feingold said.

In the meantime, Sen. Ben Nelson of Nebraska, a moderate Democrat, said he will introduce his own plan for Iraq this week. The plan would look to Gen. David Petraeus, commander of Multinational Forces in Iraq, to provide by July a baseline report on benchmarks for Iraqi government progress. Then in September, a second report would be required. The bill would not set a withdrawal timetable, but would withhold Iraqi reconstruction money if satisfactory benchmarks aren't met.

"The president has signaled he will accept reasonable benchmarks. My proposal sets those benchmarks, requires progress reports from General Petraeus and sets a financial penalty for the Iraqis in the form of withheld reconstruction funds," Nelson said.

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