I only recalled that Obama stated that he shouldn't void DADT, instead wanting Congress to do it. From this, I deduced he had the authority. But since you asked, I had to do a little research. I found this....What action could he take on DADT?
Don't ask, don't tell - Wikipedia, the free encyclopedia
I assume that Obama could give direction to the AG (Holder), whom he appointed.On September 9, 2010, Judge Virginia A. Phillips ruled in Log Cabin Republicans v. United States of America that the ban on service by openly gay servicemembers was an unconstitutional violation of the First and Fifth Amendments.[52][53] On October 12, 2010, she granted an immediate worldwide injunction prohibiting the Department of Defense from enforcing the "Don't Ask Don't Tell" policy and ordered the military to suspend and discontinue any investigation or discharge, separation, or other proceedings based on it.[54][55] The Department of Justice appealed her decision and requested a stay of her injunction,[56] which Phillips denied but which the Ninth Circuit Court of Appeals granted on October 20[57][58] and stayed pending appeal on November 1.http://en.wikipedia.org/wiki/Don't_ask,_don't_tell#cite_note-59http://en.wikipedia.org/wiki/Don't_ask,_don't_tell#cite_note-Ed_O.27Keefe-60