The real question is whether Republicans are in the mood to nominate Obama’s opposite (say, Donald Trump) or someone who is stylistically similar to Obama (say, Rubio), the way Democrats did in 1992. At that moment, the time was right for a folksy Southern Democrat who wouldn’t turn off middle America. Bill Clinton was the man for the job. Maybe the zeitgeist today calls for a cosmopolitan conservative who won’t turn off Hispanics, and millennials?
If Obama’s election actually “changed the trajectory of America,” whereby modern politicians need to be more diverse and cosmopolitan, then someone like Rubio is the GOP’s best bet. Fight fire with fire. But if Obama’s election was an anomaly, the opposite is true. (Note: My forthcoming book Too Dumb to Fail argues the former is the case. Demographic changes mean that Republicans can no longer rely solely on the votes of older, white, rural, non-college educated, married Americans. As such, I would certainly lean toward nominating someone more like Rubio than Trump.)
There are good examples for either model. After eight years, sometimes Americans crave a stark change and overreact by nominating someone the exact opposite of the last guy (stylistically, the citified Obama was vastly different from the swaggering George W. Bush). Other times, the only way political party’s can forge a comeback is by finding their own version of the other party’s guy.