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James Baker, the co-chairman of the Iraq Study Group, on Tuesday endorsed President Bush's troop surge in Iraq, urging the Senate to "give it a chance."

"The president's plan ought to be given a chance," Baker told the Senate Foreign Relations Committee. "Just give it a chance."

Baker, a former secretary of state under President George H.W. Bush, said it was wrong for the Senate to confirm Army Gen. David Petreaus to lead the new Iraq mission at the same time it was moving to pass non-binding resolutions opposing the deployment of at least 21,500 U.S. forces to improve security in Baghdad and Al Anbar Province. Some of those forces have already been deployed.

Baker also deflected criticism from Democratic senators that the president's new Iraq strategy lacked sufficient emphasis on diplomatic talks with Iran and Syria. Baker said the new plan envisions new diplomatic initiatives, though it does not include one of the ISG's chief recommendations: direct talks with Iran and Syria.

Baker's endorsement could well alter the political dynamic dealing with Senate debate on the president's new Iraq plan. Many critics have cited the ISG, which in November published 79 recommendations for getting the United States of Iraq successfully, as the basis for opposing the troop surge. References to the ISG's military and diplomatic recommendations are cited in both leading resolutions opposing the new Iraq plan.

With Baker's endorsement, opponents of non-binding resolutions may have new ammunition to argue against the Senate sending any signal of opposition to the new plan.

The ISG's other co-chairman, former Indiana Rep. Lee Hamilton, did not endorse the troop surge directly, but said the group did conditionally recommend a short-term troop surge and said the president's new plan and the overall recommendations depend on improvements pursued by the Iraqi government.

"If we can put this together there is a chance we can reasonably succeed. But we realize that is a very, very daunting challenge," Hamilton said. "There isn't any doubt that in the president's proposals and in ours that we are depending on, very heavily, an improvement in the performance of the Iraqi government. Will it happen? I don't know. It does make you uneasy, when you have to put your dependence on this government. What other alternative do you have? You can't go out on the street of Baghdad and pick 10 people and put your confidence in them."

Baker was speaking to the panel as lawmakers are challenging Bush's authority to be the decision-maker on the conduct of the war. Under the Constitution, lawmakers have the ability to declare war and fund military operations, while the president has control of military forces.

Several lawmakers have offered non-binding resolutions expressing disapproval of the Senate for the president's conduct, but some senators want to create legislative remedies that tie the president's hand. Presidents also have veto power over legislation and Bush likely has enough support in Congress on Iraq to withstand any veto override attempts

Nonetheless, Democratic Sen. Barbara Boxer of California is pushing a bill that would call for troops to come home in 180 days and allow for a minimum number of forces to be left behind to hunt down terrorists and train Iraqi security forces.

Sen. Russ Feingold, D-Wis., plans to introduce legislation that would force an end to U.S. involvement in the war in Iraq by ending funding and giving Bush six months to remove most U.S. troops.

At a Senate Judiciary Committee hearing on Congress' constitutional power to end war, Feingold said his proposal is not a way to micro-manage the war.

"It makes no sense to argue that once Congress has authorized a war it can't take steps to limit or end that war," Feingold said. "As long as this president goes unchecked by Congress, our troops will remain needlessly at risk and our national security will be compromised."

He added that by setting a limit on U.S. involvement in Iraq by using "the power of the purse, we could re-deploy our troops from that country and begin to focus on the global terrorist networks that do continue to threaten the United States."

But Sen. Lindsey Graham, R-S.C., suggested that just because Congress has the power of the purse, it should not pursue non-binding resolutions that declare the ongoing war a loss.

"It's not a question of authority, it's a question of wisdom," Graham said. "I hope the Congress is wise enough to not send a signal to our enemy that we can't stand to fight them."

Separately, Sen. Barack Obama, D-Ill., a 2008 presidential candidate, introduced the Iraq War De-Escalation Act of 2007, that he says will "not only stop the escalation of this war, but begin a phased redeployment that can pressure the Iraqis to finally reach a political settlement and reduce the violence." The plan would cap the number of troops in Iraq, and redeploy all combat troops out of Iraq by the end of March 2008 unless the Iraqi government meets certain benchmarks for political progress.

Over in the House, House Minority Leader John Boehner, R-Ohio, said Republicans will send two Iraq-related bills to the floor to serve as counter-measures to the "meaningless resolution" that Democrats intend to debate. That measure would resemble the non-binding resolution supported by Sens. Joe Biden, D-Del., and Chuck Hagel, R-Neb., disapproving the president's surge plan.

Boehner said the GOP initiatives would prohibit Congress from cutting funds for troops in Iraq and the second would create a series of benchmarks for the Iraqis to meet to ensure success in the new strategy proposed by Bush.

The Democratic resolution is likely to come to the House floor in about two weeks, and it's unclear whether the Democratic leadership will bypass committee hearings in favor of using the language developed in the Hagel-Biden plan or a less critical option by Sens. John Warner, R-Va., and Ben Nelson, D-Neb., among others.

House Majority Leader Steny Hoyer told reporters Democrats are considering pursuing a number of policy changes for the war in Iraq -- either through the appropriations or authorizations process or during review of an emergency supplemental request for war funding expected from the administration.

"We have made it very clear that we do not believe the president's proposal for increase in troops in Iraq at the levels he has proposed are going to have the effect that he says they will have. We are joined by military leaders, we believe we are joined by the (Prime Minister Nouri al-) Maliki government. We are joined by the Iraq Study Group, all of whom believe that this was not a policy that they would recommend, notwithstanding that the president is pursuing it," said Hoyer, D-Md.

FOX News' Major Garrett and Molly Hooper contributed to this report.