WASHINGTON – Two leading Senate Democrats sought to build support Sunday for a bipartisan resolution opposing President Bush’s war strategy in Iraq, cautioning that division over whether the measure goes far enough could spell defeat.

“The worst thing we can do is to vote on something which is critical of the current policy and lose it,” said Sen. Carl Levin, chairman of the Senate Armed Services Committee. “The public doesn’t support his policy; a majority of the Congress doesn’t support his policy.

“If we lose that vote, the president will use the defeat of a resolution as support for his public policy,” said Levin, D-Mich.

The new Democratic-led Congress heads this week toward its first vote on the war. The Senate Foreign Relations Committee plans to begin debate Wednesday on a resolution condemning Bush’s proposal to send 21,500 more troops to Baghdad and Anbar province. A vote could come as early as that same day.

The proposed nonbinding resolution is largely symbolic and would have no effect on money for troops. It states that “it is not in the national interest of the United States to deepen its military involvement in Iraq, particularly by escalating the United States military force presence in Iraq.”

The resolution has caused some division among Democrats who want to go further by cutting money for new troops; moderates in both parties who want softer language; and Republican leaders who have pledged to filibuster.

On Sunday, Levin and Sen. Joseph Biden, D-Del., who sponsored the resolution with Republicans Chuck Hagel of Nebraska and Olympia Snowe of Maine, said their proposal was a first step that would send a “powerful message” that Bush must change course.

Other congressional steps, such as limiting federal appropriations for the war, could come later if Bush were to continue pushing forward with additional troops in defiance of the resolution, they said.

Biden, the Foreign Relations Committee chairman, played down the notion that support could splinter over how far lawmakers should go to restrain the president’s power to wage war. He said he expected that each of the half-dozen competing proposals to oppose the war would get an airing.

“I don’t think there’s any muddled message here,” Biden said. “They’ll all get a chance to get voted on – basically all of them. And I think we’ll have some discussion.”

The proposals to limit the war vary.

Rep. John Murtha, D-Pa., and Sen. Edward Kennedy, D-Mass., say they want to cut money for new troops to prevent the deployments. Sen. Christopher Dodd, D-Conn., has a proposal that would cap troops at existing levels.

Republican Sen. Gordon Smith of Oregon said he was wary of the term “escalating” in the resolution and was working with Sens. Susan Collins, R-Maine, and Ben Nelson, D-Neb., on a “constructive, nonpartisan resolution that expresses the opposition of the Senate to the surge.”

Bush is expected to address the Iraq war in his State of the Union address Tuesday and renew his calls to work together with Democrats on a bipartisan way forward.

Earlier that day, the Senate Armed Services Committee will hear from Lt. Gen. David Petraeus, a former division commander in Iraq who was tapped by Bush to replace Gen. George Casey as the top American commander in Iraq.

On Sunday, Biden said despite the competing proposals, there was overwhelming bipartisan support in Congress against the war. He said Vice President Dick Cheney was absolutely wrong in suggesting that a resolution against the war would “embolden our enemy.”

“Every single person out there that is of any consequence knows the vice president doesn’t know what he’s talking about. I can’t be more blunt than that,” Biden said. “He is yet to be right one single time on Iraq.”

Hagel suggested there may be more Republican support than is generally known for seeking a vote in Congress toward ending the war in Iraq.

Sen. John McCain, R-Ariz., a strong supporter of additional troops, argued that much is at stake if the U.S. pulls out and Iraq is left to descend into chaos. “If we leave Iraq, I have no doubt that al-Qaida and terrorist organizations will want to follow us home,” he said.

But Sen. Patrick Leahy, D-Vt., said the war already was a failure. While a resolution against the war will send a message, only by withholding funds can Congress stop a war Bush so ardently supports, he said.

“This is the only way we stopped Vietnam,” Leahy said. “We had a lot of people who said they were opposed to it, but when we finally had a vote in April 1975, a key vote on the power of the purse, that’s what stopped it.”

Biden and Levin were on “Fox News Sunday,” McCain appeared on NBC’s “Meet the Press,” Hagel spoke on CBS’ “Face the Nation,” and Leahy were interviewed on “Late Edition” on CNN.

Associated Press writer Anne Flaherty contributed to this report.