It failed in a 57-40 test vote, falling three votes shy of the 60 needed to advance.
GOP senators demanded that the Senate vote on tax cut firsts.
"An army of allies stands ready in the House to pass a standalone repeal of the discriminatory policy once the Senate acts," she said in a statement issued Thursday.
One gay rights group, the Servicemembers Legal Defense Network, scheduled a rally Friday on Capitol Hill to show Congress it wouldn't give up.
"We must show our rage for repeal and insist the Senate stay in Washington until they have finished the job," said Aubrey Sarvis, the group's executive director.
The Associated Press contributed to this story.