Metta, thanks for giving me an excuse to go back through the NY Times archive to figure out what exactly led up to DADT. Here's what I was able to dig out about the sequence of events in 1993.
Practically from the second Clinton was sworn in, he was hit with a shit-storm from the military on his campaign pledge to allow gays to serve in the military. Colin Powell, then the Chairman of the Joint Chiefs, in particular was adamantly against it.
I think it's pretty clear that Clinton had no intention of tackling the issue so early in his term. But to give him credit, he bravely tried to stay true to his word for a while. He ordered the Pentagon to come up with a plan to repeal the ban within 6 months, and in the meantime he ordered dismissals of gay people from the military to be suspended. That idea didn't ever really fly with the Pentagon.
Then Congress weighed in, and public opinion. Both were overwhelmingly against repealing the ban. Congress held hearings, the Pentagon convened a panel, and Clinton mostly stopped talking about the issue, except when he was asked about it occasionally at press conferences.
The military and Congress spent the spring of 1993 trying to figure out how to rewrite the regulations. At one point it looked as if they would allow people to be open about being gay, but at no point did they consider lifting the ban on homosexual conduct. Clinton was asked about it on March 24, and said he supported the ban on gay "conduct", but it's not clear whether he meant gay sex or things like having a subscription to the Advocate. (At the same press conference he said he wasn't opposed to the idea of separate "homosexual units".)
The actual phrase "don't ask, don't tell" seems to have been coined by May 12. On May 28, Clinton said
"We almost have a compromise here," Mr. Clinton said in a nationally televised question-and-answer session with tourists this morning in the White House Rose Garden. "Most Americans believe if you don't ask and you don't say and you're not forced to confront it, people should be able to serve."
...
"We are trying to work this out so that our country does not -- I understand what you're saying -- so that our country does not appear to be endorsing a gay life style," he said. "But we accept people as people, and give them a chance to serve if they play by the rules."
So pretty much by then, I would say, it was all over but the shouting.
The bill that was passed specified that three things were illegal for service members: 1) homosexual conduct (unless it's something you don't usually do, the famous "I got so bombed last night I don't remember what the fuck happened" exception), 2) Openly declare you're gay, or 3) attempt to get married to someone of the same sex.
Where Clinton is being disingenous in this clip is in his statement that he had no choice but to sign the bill because it had passed by a veto-proof majority. In fact he had pretty much caved in on the issue long before the bill was passed.
But his overall point is absolutely correct. He really could not have done much more than he did, given the political climate in 1993. I also believe him when he says he never expected the military to continue or even expand their anti-gay witch hunts after DADT became law. Perhaps that shows a certain naivete on his part.
As for the idea that gay lobbying groups didn't do enough to support him, there may be some truth to that. This quote is from a New York Times article on February 24, 1993:
But for now, gay-rights groups are being criticized as having been blinded into complacency by having a President support their position. Some Congressional aides say the groups failed to muster phone banks to call members of Congress quickly, to put the gay position before the television cameras and to rally to their side representatives of other causes, like those who believe in a woman's right to choose abortion. Also, with Mr. Clinton committed to ending the ban, some Congressional figures say gay groups felt no need to shore up popular support.
