WASHINGTON (AP) — The Senate Armed Services Committee has enough votes to approve a bill overturning the ban on gays serving openly in the military, according to supporters of the effort to end the 17-year-old “don’t ask, don’t tell” policy.

The bill would still face scrutiny by the full Senate, where 60 votes are usually needed to overcome Republican objections. But an endorsement by the committee would be a crucial first step.

Several lawmakers on the panel signaled their support for the bill after a provision was included that would let the military decide when and how to implement the change in personnel policy.

Among those lawmakers was Sen. Ben Nelson, a conservative Democrat from Nebraska who had been considered a holdout.

“In a military which values honesty and integrity, this policy encourages deceit,” Nelson said Wednesday.

Nelson’s support, along with others including Maine Republican Sen. Susan Collins, meant that it was likely the measure would pass during a Thursday committee vote. That same day, the House planned to consider an identical bill.

Rep. Patrick Murphy, D-Pa., was expected to introduce the legislation as a floor amendment to the 2011 defense authorization bill.

“We are increasingly confident about the (bill) and that this could very well be a historic week in the United States Congress,” said Marshall Wittmann, a spokesman for Sen. Joe Lieberman, I-Conn., who is co-sponsoring the legislation.

The measure was more likely to survive Congress tucked into the broader defense bill, which typically includes popular provisions like a pay raise for the troops.

Gay rights groups were cautiously optimistic.

“This one will go down to the wire, and it won’t be over until the vote,” said Fred Sainz, a spokesman for Human Rights Campaign.

The legislation was a compromise between the White House and a small group of liberal lawmakers — including Lieberman and Armed Services Committee Chairman Carl Levin, D-Mich. — who fear that efforts to lift the ban would be thwarted if Republicans take control of either the House or the Senate after elections in November.

Nelson said the caveat calling for the military to decide the particulars of implementing the policy was key to his support because it “removes politics from the process” and ensures repeal is “consistent with military readiness and effectiveness.”

Defense Secretary Robert Gates has said he supports repeal but would prefer that Congress wait to vote until he can talk to the troops and chart a path forward. A study ordered by Gates is due on Dec. 1.

“With Congress having indicated that is not possible, the secretary can accept the language in the proposed amendment,” said Pentagon press secretary Geoff Morrell.

The service chiefs urged the panel not to vote until the Pentagon could interview military personnel.

“The value of surveying the thoughts of Marines and their families is that it signals to my Marines that their opinions matter,” Marine Commandant James Conway wrote in a letter to Sen. John McCain of Arizona, the panel’s top Republican.

McCain and other lawmakers, including some Democrats, took a similar stand this week and cast doubt that the measure might pass. At least one Republican — Sen. Susan Collins of Maine — has said she will support the measure.

Adm. Mike Mullen, the nation’s top uniformed officer and chairman of the Joint Chiefs of Staff, told graduating Air Force Academy cadets on Wednesday that they need to support a changing military.

Mullen didn’t speak directly about the “don’t ask, don’t tell” policy. But the chairman, who has said that the policy unfairly forces troops to lie, said service members should question convention.

“Few things are more important to an organization than people who have the moral courage to question the direction in which the organization is headed and then the strength of character to support whatever final decisions are made,” Mullen said.