Yes, Obama wants to redefine marriage. Repealing DOMA is the first step.

President Obama's Justice Department is pushing for the overturning of the Defense of Marriage Act in the courts.  DOMA defines marriage as one man and one woman for purposes of federal law and protects the right of states not to recognize same-sex "marriage" in other states.

The U.S. Department of Justice filed two petitions Tuesday as part of their challenge to the Defense of Marriage Act, asking the Supreme Court to review cases that could ultimately lead to the court overturning the law that defines marriage as between and man and a woman.

The specific part of the law that attorneys for the Justice Department want the court to focus on is Section 3, which they say violate the rights of legally married same-sex couples, arguing that it treats them differently than married heterosexual couples.

...Additionally, the Justice Department also wants the court to review a case involving six same-sex married couples and a widower from various states that were denied federal benefits. In all, the U.S. Supreme Court has been asked to review four cases that could eventually lead to part or all of DOMA being ruled unconstitutional given that federal courts in several states have issued such opinions.

Another important implication of November's election.