As the Senate heads toward debate next week over President Bush's Iraq war plans, even some senators are questioning whether the proposals on the table — nonbinding resolutions critical of the president — will have any impact.

"This vote will force nothing on the president, but it will confirm to our friends and allies that we are divided and in disarray," Sen. Richard Lugar, the Senate Foreign Relation Committee's top Republican said Wednesday before a vote by the panel on various senses of the Senate.

"It's the wrong tool for this stage in the Iraq debate. It is unclear to me how passing a nonbinding resolution — that president has said he will ignore — will contribute to any improvement or modification of our Iraq policy.

"Its passage will not benefit U.S. policy and it may actually harm the policy making process," Lugar said, who added that he's not at all confident the president's strategy will succeed and called "dubious" the idea that clearing out terrorists from the high-risk areas in Baghdad will give the Iraq government enough room to force political reconciliation.

Despite Lugar's objection, the Democratic-led panel approved on 12-9 vote a resolution that says the president's war plan is a "not in the national interest ... particularly by increasing the United States military force presence in Iraq."

The resolution is co-sponsored by Chairman Joe Biden of Delaware, as well as Sens. Chuck Hagel, R-Neb., and Carl Levin, D-Mich. Hagel was the only Republican to vote for the measure.

Another measure co-sponsored by Sens. John Warner, R-Va., Ben Nelson, D-Neb., and Susan Collins, R-Maine, is seen as a softer approach but still disagrees with the president's plan to send 21,500 more troops into Iraq. It also calls on the president to revisit the Iraq Study Group proposal, among other things.

Introducing the resolution on Monday, Warner said he was taking up the president's suggestion that critics offer a better plan rather than just disagreeing with him.

"I accept the president at his word. He did it not once, not twice, but I know of three times where he has said on national television and otherwise, 'I will listen to the ideas of others,' " Warner said.

On Wednesday evening, Warner and his allies announced seven additional co-sponsors for their resolution, which they say they expect to offer as a substitute to the Biden-Hagel-Levin resolution. Floor action is expected to begin next week.

Supporters say that if a majority of Congress approves either one of the competing resolutions, it will send Bush a strong message.

"My experience with this administration after six years is — and maybe yours is different — is the only way to get its attention is to make it crystal clear, crystal clear and publicly clear, that you take issue with what they're proposing," Biden said.

But the White House so far hasn't given any indication that a vote by the Senate would change the president's Iraq plans.

"The president is commander-in-chief. It is his constitutional obligation to keep the country safe. And he believes his way forward is the effective way to do it," White House spokesman Tony Snow told FOX News.

Republican strategist Pete Snyder said many of the resolutions' supporters, especially 2008 presidential candidates, are running "far, far away" from the president because "that's what happens when you're in your 30s on your approval rating."

Snyder said a leadership vacuum in the country means politicians are going to try to put up bold plans and clear directions, but until then, the resolutions don't stand for much.

"It's certainly good politics for the Democrats to keep on bringing this up. So I am sure you are going to have resolution after resolution. They are going to be grabbing as many headlines as they can, but ultimately it's going to mean nothing," he said.

Some lawmakers are jockeying for stronger measures than resolutions. Sens. Russ Feingold, D-Wis., and Edward Kennedy, D-Mass., have separately proposed legislation aimed at binding the president's hands. Biden said Thursday that he didn't think any proposal stronger than a resolution could beat back a filibuster-proof 60 votes.

"This is clearly in the hands of the administration and of the president. Sure, Congress can pass all sorts of resolutions until they are blue in the face, but the only power they have is over the purse string," Snyder said.