Okay my answer to the question
can a republican win the next Presidential election, is yes.
Now if you had asked if I thought it was likely a repuke would win, I would take the easy way out and say maybe.

I would like to think another 4 years of 8% unemployment and deficits as far as the eye can see, and all the new taxes coming at us, that the democrats would be an endangered species for awhile, but after witnessing what happened in November I doubt it.
2 reasons I think the GOP winning, (notice I didn't say us), is not likely are,
1:whoever runs will run on 0bama's record of freebies for all, and people will probably want to protect 0bama's legacy by not putting a repuke in office, 2:considering how the GOP is acting now, they will be running a progressive in 2016 and conservatives will stay home.