Senators also voted to endorse the Bush administration's military tribunals for prosecuting foreign terrorism suspects at the U.S. naval base at Guantanamo Bay, Cuba, but to allow the detainees to appeal their detention status and punishments to a federal court.
On the question of a timetable for troop withdrawal, senators rejected the Democrats' proposal by 58-40. Democratic leaders had advanced the measure in the wake of declining public support for a conflict that has claimed more than 2,000 U.S. lives and cost more than $200 billion.
Republicans countered with their own nonbinding alternative urging that 2006 "should be a period of significant transition to full Iraqi sovereignty." That GOP provision was approved by the Senate on a 79-19 vote, with five Democrats siding with the majority party.
The Republican version was actually pretty similar to what Democrats wanted, reports CBS News correspondent Bob Fuss. It asks for reports and suggests outlines of a policy to be laid out to set markers and urge the Iraqis to understand they have to solve their own problems. What it didn't have was any demand for timetables for bringing troops out.
"They want an exit strategy, a cut-and-run exit strategy. What we are for is a successful strategy," said Senate Majority Leader Bill Frist, R-Tenn.
Senate Democratic leader Harry Reid, D-Nev., said: "We want to change the course. We can't stay the course."
Tuesday's fast-paced developments underscored the political significance of the war as the U.S. death toll climbs, public support plummets, the insurgency continues and the price tag soars with no end in sight.
CBS News' Aleen Sirgany reports that when speaking, Sen. Joe Biden, D-Del., directed to President Bush: "Tell us the plan, Stan. Tell us, Mr. President, what is the plan?"
The Senate added the Iraq policy to a defense bill the Senate approved on a 98-0 vote Tuesday.
Overall, the bill includes provisions that, taken together, mark an effort by the Senate to rein in some of the wide authority lawmakers gave the president following the Sept. 11, 2001, terrorist attacks.
The measure includes White House-opposed language that would prohibit the cruel, inhuman and degrading treatment of detainees and standardize interrogation procedures used by U.S. troops. The Bush administration has threatened to veto any bill that includes language about the treatment of detainees, arguing it would limit the president's ability to prevent terrorist attacks.
Senators added the language Tuesday that would allow Guantanamo detainees to appeal their status as "enemy combatants" and the rulings of U.S. military tribunals to a federal appeals court in Washington, D.C. That avenue would take the place of the one tool the Supreme Court gave detainees in 2004 to fight the legality of their detentions — the right to file habeas corpus petitions in any federal court.