Senate Democrats said Sunday they might try to restrict President George W. Bush's ability to wage war in Iraq by approving a more limited version of the 2002 measure that authorized the use of force against Saddam Hussein. A top Republican doubted the idea would have enough support to pass. After a week of contentious debate in Congress on Bush's war strategy, the White House scoffed at Senate Majority Leader Harry Reid's claim that US-led invasion in March 2003 has become "the worst foreign policy mistake" in US history. "The war is tough, but the solution is not to get out. It is to provide the kinds of resources and reinforcements our forces need to get the job done, and at the same time say to the Iraqis `You guys got to step up,"' press secretary Tony Snow said. Two Democratic Senate committee chairmen spoke of possibly modifying the 2002 resolution that authorized Bush to go to war. "That was a wide-open authorization which allowed him to do just about anything and put us now deep into combat in Iraq," said Sen. Carl Levin, who heads the Senate Armed Services Committee. "We can modify the authorization in order to provide a much more limited mission which will remove our troops from the middle of a sectarian civil war," said Levin. Sen. Joe Biden, a 2008 Democratic presidential candidate who leads the Senate Foreign Relations Committee, spoke of repealing that original authorization and restating the president's authority, to clarify the current mission of US troops in Iraq. "I've been working with some of my colleagues to try to convince them that that's the way to go ... make it clear that the purpose that he has troops in there is to, in fact, protect against al-Qaida gaining chunks of territory, training the Iraqi forces, force protection and for our forces," said Biden. Yet the top Republican on Biden's committee, Sen. Richard Lugar, said he did not think such a measure limiting the commander in chief's ability to wage war had a chance of passing. "I think the president would veto it and the veto would be upheld. I think the point that Senator Biden making, however, is that there is public pressure. Certainly, public opinion is out there that influenced the votes that we have just seen," said Lugar. He said he thinks "the president is paying attention" to what is going on in Congress, even though the resolutions debated are non-binding. "Perhaps the president's situation is improved if he calls on key members of Congress and says, `We're in a situation of rather fractured political circumstances right now. And we need to think through this situation.' I think that would be very, very helpful," Lugar said. Snow said it was important to remove Saddam from power and noted that a majority of senators voted in 2002 to authorize force in Iraq. He said Bush should not see votes in Congress in opposition of his new Iraqi strategy as a rebuke. "The strategy has barely had a chance to begin working," Snow said. The House passed a non-binding resolution Friday that rejected the president's 21,500-troop buildup in Iraq. The vote put Bush on the defensive going into a far more consequential confrontation over paying for the plan. On Saturday, Senate Republicans foiled a Democratic bid to repudiate Bush's deployment of additional combat troops. The 56-34 vote fell four short of the 60 needed, but Democrats quickly claimed victory, noting that a majority of senators voted against the escalation. "This war is a serious situation," Reid said Saturday. "It involves the worst foreign policy mistake in the history of this country. ... We find ourselves in a very deep hole. We need to find a way to dig out of it." Snow said the president understands the importance of debate about the war on Capitol Hill and understands lawmakers' anxiety about the war. "What I would say to members of Congress is: Calm down and take a look at what's going on, and ask yourself a simple question: If you support the troops, would you deny them the reinforcements they think are necessary to complete the mission?" House Democrats have said they will attempt to place restrictions on Bush's request for an additional $93 billion for the military in an effort to make it impossible for him to deploy all 21,500 additional troops. Democratic Rep. John Murtha has described a series of provisions that would require the Pentagon to meet certain standards for training and equipping the troops, and for making sure they have enough time at home between deployments. Republicans say the effect would be to deny troops needed reinforcements and are expected to try to block the restrictions. Levin was on "Fox News Sunday," Snow appeared on CNN's "Late Edition," and Biden and Lugar were interviewed on "Face the Nation" on CBS.