All Republican candidates have said they will have the court revisit this case within the first year. Trump says he will have it done in the first month. Cruz, first day.
In their wildest dreams.
There's no injury-in-fact, no standing, no original jurisdiction with the Supreme Court. Who the hell would they sue as the defendant? United States v. ? United States? Supreme Court? Would they pass a new DOMA to force a new showdown? With 40 democratic members in the Senate that ain't going far.
That being said, if I was a conservative president, didn't give a shit about the rule of law, didn't care about blowback from the liberal parts of the country I'd do the following (assuming I have majorities in both houses):
1) I'd immediately have congress pass a law expanding the Supreme Court to 15 justices.
1b) I'd have Hatch exercise the nuclear option to push it through the Senate.
2) I'd nominate anti-gay, ultra-conservative justices to pack the Supreme Court
3) Pass a new DOMA.
4) Wait for some gay couple to sue.
5) Watch as the shit hits the fan and Obergefell is overturned.
In all practicality, this is settled law. There's no "revisiting" a supreme court decision without a controversy. To show a controversy you need to show harm. Thinking that gays are icky and that god hates them getting married is not harm.