Timothy Kincaid explains what would likely happen:
The House of Representatives has a small window in which to decide whether to defend DOMA in court. Should they fail to do so, then in March the courts will be presented with a motion for summary judgment (a request for a trial-less determination) which argues that DOMA Section 3 is unconstitutional, and in response the DOJ will say, “I got nothing.”
Presented with only one side, it is extremely probable that the judges will find for the plaintiffs and order the federal government to recognize their marriages. This could be limited to specific circumstances for individual plaintiffs or applied broadly against the United States and applicable to all same-sex marriages. However, without appeal to the US Supreme Court, then these decisions will only apply to same-sex married couples in Second Circuit states (Connecticut, Vermont, New Hampshire, and New York).