The Pentagon is actually already in the process of asking questions about how repealing "Don't Ask, Don't Tell" would affect the military. It's just that Obama and some congressional Democrats want Congress to vote to repeal DADT now, before Congress has answers from the Pentagon's year-long review on how repealing DADT would affect military readiness, military effectiveness, unit cohesion, and recruiting and retention.
Repeal would go into effect once Obama, Secretary Gates, and Chairman Mullen sign off on the Pentagon's review.
But the whole point of the review was to determine how repeal would be implemented before Congress voted on repeal. As Virginia's Democratic senator Jim Webb said at the February 2 Senate hearing on DADT with Gates and Mullen:
"this year period that you're going to take in order to examine the issues will be followed then by clearer observations about the implications of changing the law. Would that be a correct way to state it? So you're not coming in here today and saying, we're going to change the law and this is the year that we're going to put into figuring out how to implement the change?"
Gates replied in the affirmative: "Our hope would be that the information we would develop during the course of this review would help inform the legislative process."
"Right," said Senator Webb. "I salute both of you for very careful statements."
Webb continued: "what we're looking for here is an examination of the present law. What is the most damaging aspect of the present policy? ... And then, again, what are the perils of undoing the law? Where are we going? Do we -- would we know we were going in the proper direction? We don't -- we can't really say that today. ... whether the ultimate decision might be here with the Congress, that decision can't be made in a proper way without a full and open input from all of those who are serving. Not just combatant commanders -- family members, people who are in the operating units."
Again: Congress was supposed to weigh the Pentagon's report on how repeal of DADT would be implemented first--and then vote for or against repeal. It remains to be seen if Webb and other Democrats on the Senate Armed Services Committee still believe they have the responsibility to assess the Pentagon's report before voting on repeal.
Carl Levin needs 15 senators to vote the bill out of committee. I'd guess the Democrats who may be on the fence include Webb, Ben Nelson, and Robert Byrd (I would have included Evan Bayh if he were up for reelection). Republicans who may be open to repeal include Lindsey Graham, Scott Brown, and Susan Collins. But you'd think they would at least support a full and informed debate on DADT before bringing it to a vote.
Update: This post has been updated to clarify that the Pentagon would simply report on how repeal would be implemented. It would be up to Congress to then determine how detrimental or beneficial repeal would be.