I think you are wrong in this. Climate change may become a dominant issue, but the Republican presidential candidate will not move toward accepting it. He will deny it even more vehemently.I predict global warming/climate change will become a dominant issue in the 2016 elections.
However "misguided" you may think it is to believe the facts, Republican presidential candidates will move toward acceptance of AGW science in an attempt to get more votes.
That is because the coalition of economic Libertarians and the Christian Right that now control the Republican nominating process are the most ardent of deniers. Too, they have bundled a group of separate issues, one of which is the conviction that global warming is either a hoax or that it is good, into something that resembles a religious creed. You cannot change or deny one part of the creed without denying or changing all of it. Anybody that tries to change the stand on global warming will be cast as unreliable on the other issues, such as opposition to abortion.
I am betting that the Republican presidential nominee will be Kentucky's Senator Rand Paul. He will lose the general election. However, the Bible Belt states will elect a solid slate of Tea Party type "conservatives" to the House and Senate. There won't be enought of them to actually pass any of their legislative agenda, but there will be enough to produce deadlock. They will get what the minimalist government that they want by paralyzing the governing process.
Things will have to get really, really bad before the grip of the preachers who now call the shots in the Bible Belt either change their tune or lose their influence. I'd guess the time scale at 12 to 15 years before there is any substantial change in the way people in the Bible Belt think and vote. By then we will be well on the way to 500 ppm CO2, an ice-free Arctic, and quite likely past the point of no return to a disastrous rise in sea levels and change in weather patterns.