I am guessing that the democrats will put it up for a vote, knowing that almost all republicans will vote against it, but probably the republicans who control the house, will prevent it from being put up for a vote there. Note that in the Judiciary Committee today, every single republican voted against repeal.
The Democrats, of course, could have passed a repeal of DOMA when they controlled both houses for the first two years. Obama would probably have vetoed if it had been passed - like Bush, he is too much guided by religion. Also let us not forget that it was Clinton who gave us DOMA in the first place, along with Dont Ask Dont Tell. No love here for the democrats, who save for Barney Frank, only want our money. We should also not forget, that when Obama was running for the senate, he said he supported the right of gays to marry. Of course, during his presidential campaign, he reversed his position and said he was opposed to same sex marriage.
It will probably be up to the court. Too bad that the Dino Feinstein and others did not prevent reactionaries Roberts and Alito from being confirmed.