Adam Serwer has a few thoughts on why the Right doesn't want to mix it up over DADT:
The answer is that most of the country supports repealing DADT, and Republicans aren't eager to get into a fight that public opinion doesn't support them on and that will redefine the GOP as the party of homophobes for another generation. The other day Jonah Goldberg was fretting and doing backflips to avoid stating the obvious, that a debate over DADT would inflame the substantial homophobic presence in the Republican Party:
Obama wants to win back independents. And while I doubt that independents care very much — at least right now — about the issue, they also don't like big fights over gays. Stirring-up social conservatives and eliciting the inevitable harsh soundbites from, say, Pat Robertson would provide the White House with an opportunity to reprise the anti-talk-radio storylines of early last year (remember the whole White House v. Limbaugh fuss?). Whatever the merits of the issues, and fair or not, independents tend to blame conservatives for those sorts of debates.
Unlike marriage equality, the American people seem pretty straightforward on DADT: Not allowing gays and lesbians to serve openly is bigotry. They're uncomfortable with that. And the GOP is uncomfortable with cementing the impression that they are homophobes who aren't simply comfortable "maintaining the traditional definition of marriage" but really want to exclude the LGBT community from as many aspects of public life as possible.
Goldberg concluded that "Obama and Pelosi aren't actually going to do anything about Don't Ask, Don't Tell for the foreseeable future." Congressional hearings on repealing DADT start tomorrow, and in the meantime Defense Secretary Robert Gates has barred the discharge of service members "whose sexual orientation is revealed by third parties or jilted partners."