The policy prohibits gays and lesbians from serving openly in the military.
The Obama administration has urged the Supreme Court not to get involved at this point. The president has pledged to push lawmakers to repeal "don't ask, don't tell" before the new Congress is sworn in.
Last month, a federal judge ruled that the policy violates the civil rights of gays and issued an injunction barring the Pentagon from applying it. Then an appeals court said the policy could remain while it considered an appeal.
The Associated Press contributed to this story.