I think this is potentially good news for repealing the Don't Ask Don't Tell policy (DADT). Why? They don't seem to be related. Bear with me.
Obama is currently spending a lot of political capital. He has been spending it for several months now. That's normal for a president early in his term. But what is also normal is that they don't get much of a return on spending that political capital until later.
Obama is spending massive amounts of political capital. He needs to spend massive amounts more, particularly on solving the Israel-Palestine problem. But he hasn't gotten any return on any of this spending of political capital yet. We don't know if the stimulus is working. GM and Chrysler are bankrupt, and we have no idea if they will be able to come back. We are still in Iran and Afghanistan. We are running huge deficits.
Putting Sonia Sotomayor on the Supreme Court will require spending very little political capital on Obama's part, but will deliver great returns. He doesn't really have to spend any political capital. Hispanics will be forever grateful to him for this. She will probably be on the Court for decades.
But changing DADT will be the exact opposite political equation: it will require large amounts of political capital, and will deliver good, but probably not great, returns. Gays and lesbians are mostly already in his court. They will be disappointed if he doesn't deliver on repealing DADT. OTOH, some moderates and conservatives will be upset about it. Obama is going to have to spend not just a fair amount of political capital changing it, but a fair amount of his time, as well. He is going to have to lay the groundwork. He is going to have to make it a priority.
Before he can spend that kind of political capital, Obama needs a return on the investment of political capital that he has already spent. Which is where Sotomayor comes in. Putting her on the Court will be one of his first major victories, a very early return on spending political capital.
More importantly, Sotomayor represents a victory over the obnoxious idiots dominating the conservative mediaspace right now. Newt Gingrich, a man who was washed up 10 years ago, is making headlines. He is spending some of his own political capital opposing Sotomayor and Obama.
Let's imagine that Sotomayor gets 80 votes in the Senate. Not an unreasonable supposition. That's a solid victory for Obama. Now let's suppose she gets 90 votes, because, honestly, there's really not much reason to oppose her. That's a decisive victory for Obama. Moreover, it's embarrassing for Gingrich and other conservative activists, because they will have spent time and energy on a hopeless and futile cause. And a black guy with a funny name, and a Hispanic woman, will have achieved a historic victory over some stupid white guys. That will marginalize Gingrich and Limbaugh, and make Republicans in the Senate slightly more wary of taking on Obama on social and cultural issues.
I don't know how much political capital Obama will spend on repealing DADT after Sotomayor's confirmation. He does have to take it on at some point. But I am fairly confident that he won't even get seriously started until that vote is taken to put the first Hispanic woman on the Supreme Court.