NOTHING. DO ABSOLUTELY NOTHING.
Or to put it differently: dare the GOP to refuse to raise the debt limit.
Consider each scenario:
(1) Obama invokes the 14th Amendment and/or the platinum coin option. The result? Our national circus escalates to new heights, with impeachment a possibility. Eventually, the debt limit gets raised, but months are wasted, perhaps endangering some of Obama's initiatives on immigration, guns, etc. While he ultimately prevails on the debt limit, Obama receives a firestorm of criticism from the mainstream media for using gimmicks in furtherance of a "power grab."
(2) Obama simply follows through with his vow not to negotiate over the debt limit. The result? At first, a handful of prominent GOP congressmen make noises about not raising the debt limit, which leads to a growing chorus of criticism without and outside of the party. The GOP then folds and raises the debt limit as scheduled, or does so shortly after going over the deadline and causing riots in the street (well, not literally, but you know what I mean). Whatever damage occurs to the system gets roundly blamed on the GOP. If the damage is great enough, the GOP gets routed in 2014. Meanwhile, Obama earns plaudits from friends and foes for holding firm, and declining to resort to "gimmicks," perhaps easing the passage of other legislation later in the year.
Really, people, I don't think the choice is difficult at all.