The White House and leading lawmakers came to an agreement Monday about how to end the ban on gays and lesbians serving openly in the military, likely speeding the end of the "don't ask, don't tell" policy. Backers were optimistic that they could this week attach the amendment to a broader defense funding bill expected to pass this year.

The bill wouldn't immediately repeal the Clinton-era policy. Rather, it would take effect as soon as a Pentagon review is complete and the president signs off on the military's recommendations...