Story Highlights• Handful of Republicans oppose troop increase; Lieberman offers support
• Obama: Speech lacked strategy for "political accommodation" in Iraq
• McCain: Troop increase sufficient; "I do believe we can win"
• Hagel: "This is a dangerously wrong-headed strategy"
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WASHINGTON (CNN) -- Democrats generally reacted with disdain and Republicans with cautious support Wednesday night after President Bush laid out his plan to increase U.S. troop strength in Iraq.
But some Republicans crossed party lines in opposition to Bush's plan, while Sen. Joseph Lieberman offered support.
Delivering the Democrats' official response from the Senate Gallery, Illinois Sen. Dick Durbin said, "Escalation of this war is not the change the American people called for in the last election." (Watch Democrats list reasons they oppose Bush's new plan )
Speaking from the White House Wednesday night, Bush said he will increase American forces by more than 20,000, most of them in Baghdad. (Full story)
Durbin said Bush's plan ignores the advice of his own top generals, including Gen. John Abizaid, the outgoing chief of U.S. forces in the Middle East.
Durbin, the majority whip, called for the "orderly" withdrawal of troops from Iraq to send the Iraqis the message that the United States will not perpetually back them militarily.
"Every time they call 911, we are not going to send 20,000 more American soldiers," Durbin said.
He rejected the notion that the basic solution in Iraq is a military one.
"If there's any surge that's needed in Iraq, it's a surge in diplomacy," Durbin said. (Read all of Durbin's remarks)
Illinois Democratic Sen. Barack Obama, a possible 2008 presidential candidate, told CNN's "Larry King Live" that he "didn't see any political strategy in the president's remarks to get Sunni and Shia to arrive at the political accommodation" necessary for peace.
Obama said he would rather see troops redeployed to "Afghanistan and other areas where we can fight the battle against terrorism and al Qaeda."
"The burden of proof is now on the administration and the Iraqi government to show they can now make progress," he said.
Another possible Democratic presidential contender, New York Sen. Hillary Clinton, said Bush's Iraq policy "has been marred by incompetence and arrogance."
"He will continue to take us down the wrong road -- only faster," she said.
Former Sen. John Edwards, who is running for the Democrats' 2008 presidential nomination, said "the trust in the president has eroded."
"I think escalating the war is a huge mistake," Edwards told CNN.
It wasn't just Democrats coming out against Bush's plan.
Sen. Chuck Hagel, a Nebraska Republican, said, "This is a dangerously wrong-headed strategy that will drive America deeper into an unwinnable swamp at a great cost."
"We should be focused on helping the Iraqis find a political solution and creating a policy that allows us to leave Iraq honorably, has the sustained support of the American people and does not further destabilize the Middle East," Hagel said.
Support for president's strategy
The president had his supporters, too. (Watch Bush cite 'mistakes,' outline new plan )
Lieberman, who calls himself an "an independent Democrat," applauded Bush "for rejecting the fatalism of failure and pursuing a new course to achieve success in Iraq."
Sen. Lindsey Graham, a South Carolina Republican, called Bush's plan "a much-needed change."
"I appreciate his willingness to acknowledge past mistakes and chart a new course to achieve victory in Iraq," Graham said.
Republican Sen. John Cornyn of Texas scorned some Democrats' call to withdraw troops.
"Simply abandoning Iraq now, as some would have us do, would ensure failure and put America's national security at risk," Cornyn said. "The strategy presented tonight represents a real opportunity for peace and stability in Iraq."
Sen. John McCain, an Arizona Republican and a likely presidential candidate, said a fundamental problem all along has been a lack of sufficient forces. But he said on CNN that Bush's plan should solve it.
"We are paying a very heavy price for it," McCain said. "But I do believe we can win."
McCain, who as recently as last week had advocated sending as many as 35,000 more troops to Iraq, said earlier Wednesday he is satisfied with Bush's plan.
Other Republicans were wary of the plan but not willing to cut off funding as a way to stop it.
"This is the president's Hail Mary pass. Now it is up to the Iraqi Army to catch the ball," Sen. Gordon Smith, an Oregon Republican, said.
"We are extending an ineffective tactic to further the status quo," Smith continued. "Iraqis must be the ones to settle their own peace." (Watch whether Bush's "last chance" stands a better chance )
Before Bush's speech, Ohio Republican Sen. George Voinovich said he was "skeptical that a surge in troops alone will bring an end to sectarian violence and the insurgency."
Voinovich said he would make up his mind after Senate hearings in the coming weeks.
Democrats say input not sought
House Speaker Nancy Pelosi and Senate Majority Leader Harry Reid complained that they were not consulted on the plan.
"This was notification, not consultation," Pelosi said after Democratic leaders met with the president Wednesday afternoon.
In addition, Reid said, the briefing didn't help him understand how the new policy will be successful.
"I am at a loss as to what is going to happen with the additional troops," he said.
House and Senate Democrats said that rather than moving to block funds for the troop increase, they will take votes on nonbinding resolutions opposing the increase.
"Next week, the plan is to draft a very simple resolution asking the members of the Senate if they support or do not support this surge," Sen. Charles Schumer, a New York Democrat, told reporters. "I believe there will be a strong majority against it, including some from the other party."
A final vote on the Senate resolution might not take place until after Bush's January 23 State of the Union address, a Democratic leadership aide said.
Three other senators formally declared their opposition to the plan earlier Wednesday. Moderate Sens. Norm Coleman, a Republican from Minnesota, and Max Baucus, a Democrat from Republican-leaning Montana, delivered speeches on the Senate floor.
"America entered into this war with motivations that were honorable, but they were mistaken," Baucus said. (Watch what the war is costing American taxpayers )
Coleman said: "If Iraq is to fulfill its role as a sovereign and democratic state it must start acting like one. I oppose the proposal for a troop surge in Iraq, where the violence can only be defined as sectarian."
Kansas Sen. Sam Brownback, a conservative Republican and likely presidential candidate, met with Iraqi Prime Minister Nuri al-Maliki in Baghdad earlier this week.
"I came away from these meetings convinced that the United States should not increase its involvement until Sunnis and Shia are more willing to cooperate with each other instead of shooting at each other," Brownback said in a statement.
CNN's Ted Barrett, Dana Bash, Lisa Goddard and Suzanne Malveaux contributed to this report.
Illinois Sen. Dick Durbin, speaking on behalf of Democrats, said, "The president's plan moves the American commitment in Iraq in the wrong direction."