"It's in their best interest to become part of the solution instead of sitting on the sidelines," the Ohio senator said of the Iraqi people. "I don't think they'll get it until they know we're leaving."
Voinovich's remarks come on the heels of similar comments by Sen. Richard Lugar, R-Ind. The two GOP senators previously had expressed concerns about Bush's decision to send 30,000 extra troops to Iraq in a massive U.S.-led security push in Baghdad and Anbar province. But they had stopped short of saying U.S. troops should leave and declined to back Democratic legislation setting a deadline for troop withdrawals.
The strong words of these two moderate Republican senators could provide cover for even more Republicans, which is why this challenge to Mr. Bush is such a big deal, reports CBS News chief White House correspondent Jim Axelrod.
"In many ways it is the moderate Republicans who may provide the grist and the number of votes needed to create veto-proof legislation mandating a troop reduction," says Michael O'Hanlon, a senior fellow at the Brookings Institution.
Lugar and Voinovich said they are still not ready to insist on a timetable for withdrawal. But they both made it clear their patience was gone.
Voinovich said he was presenting his proposal for a way out of Iraq in a letter to the president, slated for release later Tuesday.
Once Iraq's neighbors "know we are genuinely leaving, I think all of a sudden the fear of God will descend upon them and say, 'We've got to get involved in this thing,"' he said.
"It can't be something that is precipitous, but I do believe that it should be enough so that people know we are indeed disengaging," Voinovich said.
The loss of GOP support for the president's strategy is significant. Democrats may still not be able to push through legislation demanding an end date to the war, but softer alternative proposals are in the works that could still challenge Bush.
After the Fourth of July recess, "you'll be hearing a number of statements from other (Republican) colleagues," predicted Sen. John Warner, R-Va., a longtime skeptic of the war strategy.
Spokesman John Ullyot said Warner is drafting a legislative proposal on the war, but declined to discuss the details. The measure would likely be offered as an amendment to the 2008 defense authorization bill on the floor next month.
The White House on Tuesday appealed to members for more patience on the war in Iraq.
"We hope that members of the House and Senate will give the Baghdad security plan a chance to unfold," said White House spokesman Tony Snow.
Snow also said Lugar was a thoughtful man and that his remarks came as no surprise.
"We've known that he's had reservations about the policy for some time," he said.
In January, Lugar expressed concerns about the president's decision to send 30,000 extra troops to Baghdad. But he voted against a resolution opposing Bush's troop build up, contending that the nonbinding measure would have no practical effect. In the spring, he voted against a Democratic bill that would have triggered troop withdrawals by Oct. 1 with the goal of completing the pullout in six months.
In a floor speech Monday, Lugar said the U.S. should reduce the military's role in Iraq and called on Bush to press other diplomatic and economic initiatives instead. Because of Lugar's position as the top Republican on the Foreign Relations Committee, his speech was a considered a blow to the administration as it tries to shore up sagging political support for the unpopular war.
"In my judgment, the costs and risks of continuing down the current path outweigh the potential benefits that might be achieved," Lugar, R-Ind., said in a Senate floor speech. "Persisting indefinitely with the surge strategy will delay policy adjustments that have a better chance of protecting our vital interests over the long term."
Senate Majority Leader Harry Reid called Lugar's speech "brilliant" and "courageous" and said it would later be noted in the history books as a turning point in the war.
"But that will depend on whether more Republicans take the stand that Sen. Lugar took," added Reid, D-Nev.