Several analogues have been drawn between Richard Nixon and Barack Obama on this site. If these analogues extend to President Obama's successors, a moderate Republican governor could be elected in 2016 (Chris Christie) only to face a stagnating economy and deteriorating foreign relations and be replaced by a charismatic Democratic governor (Andrew Cuomo or Gavin Newsom) in 2020. Just some food for thought...
There have been some comparisons between Carter and Christie. I think there is some merit to this. Lots of people across the political spectrum like Christie, but very few love him. I could see the Republican base abandoning him if the economy faltered. And if he does win in 2016, he would do it with a very different coalition/EC map than most winning Republicans. I just don't know if he can get past Clinton, though.
Finally, a Democratic Reagan would have to be someone who is currently a bit too left wing to be taken seriously. Newsom is a possibility, but Cuomo is way too mainstream and moderate. Elizabeth Warren is probably the most obvious candidate to advance a Newer Deal, but she would be in her 70's by 2020.
The thing about Reagan though was that even though he style was clearly conservative, his substance was more a mixed bag. Reagan did raise taxes in California and sign an assault weapons ban as Governor. If Cuomo could significantly alter his rhetoric to make it strikingly more liberal, I could see him doing quite well in a Reagan-type mold. Of course, Reagan has a much more aggressive leadership style than I think Cuomo does.
Moreover, the Democrats may be more apt to pick a Senator as their "Reagan" rather than a governor, as that is their historic predisposition. In that case, I think that Tim Kaine, Martin Heinrich, Mike Bennett, or Bruce Braley if he can get elected to IA Senate in 2014.