Gay rights activists are gearing up for a Thursday vote on a measure to end the military's "Don't ask, don't tell" policy.

The Human Rights Campaign (HRC), a leading lesbian, gay, bisexual and transgendered (LGBT) advocacy group, said it expects a vote to come up Thursday on an amendment to a defense authorization bill that would end the military's long-standing prohibition on gay and lesbian servicemembers serving openly in the military.

HRC said Monday that it expects the amendment to come up for a vote concurrently on Thursday, one time on the House floor and one time in the Senate Armed Services Committee.

The group is focusing on six key centrists — five Democrats and one Republican — who sit on the Senate committee ahead of the vote. The target senators are Robert Byrd (D-W.Va.), Bill NelsonClarence (Bill) William NelsonReport: FCC chair to push for complete repeal of net neutrality Collins: Pass bipartisan ObamaCare bills before mandate repeal Democrats scramble to contain Franken fallout  MORE (D-Fla.), Ben Nelson (D-Neb.), Evan Bayh (D-Ind.), Jim Webb (D-Va.), and Scott Brown (R-Mass.).

The group is targeting the senators by deluging their offices with phone calls and other grassroots signs of support, including thousands of signed post cards and rallies planned in their states. Ben Nelson has said he plans to oppose repealing the policy.

Gay rights activists have expressed frustration with President Barack ObamaBarack Hussein ObamaReport: FCC chair to push for complete repeal of net neutrality Right way and wrong way Keystone XL pipeline clears major hurdle despite recent leak MORE, who has pledged to end the policy, and with some congressional Democrats for the pace at which they have worked to get rid of the policy.

House Speaker Nancy Pelosi (D-Calif.) last week vowed to do away with the policy by the end of this year.