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human
I believe the Republican Party will die within the next 100 years and will be replaced by the Libertarian Party. CMV

It has recently become fairly clear that the Republican Party is clearly disconnected with the younger generation.  Millennials are increasingly more skeptical of religion and very supportive of gay rights and action on climate change.  They also view the Republican Party as out of touch with reality and old fashioned.  I predict that within the next couple decades, Republicans will show a deep decline in support within the American Populace.  However, Republican backers have some very deep pockets.  Therefore, they will continue to win elections (particularly in districts where apathy is rampant and incumbents have been there for a long time) and maintain a presence for quite some time. They will ultimately accept their fate and rebrand themselves as libertarians that support common sense answers to the social issues afflicting us today.  The Republican platform has little to no merit with younger people except in terms of economic issues.  While I happen to disagree with libertarians stance, it will be far more tolerable that the GOP we see today.  CMV

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gpt
It's far more probable that the Republican party will survive, but will shift towards a more libertarian stance - if libertarianism is what will get them votes. Political parties are notoriously hard to ruin, especially in a two-party system. No matter how much people gripe about them being out of touch, they still have a sizable base, and new blood from a younger generation, like Marco Rubio for example, will be on the forefront of changing the party to be more on line with a changing society. 

Think about how Republican party lines are already changing due to demographics (immigration reform instead of more border policing and building an ineffectual fence) and the now majority acceptance of LGBTs. Just remember that Republican politicians are still politicians at their heart. Maybe they'll need to lose a few more presidential races, and lose the popular vote a couple more times, but they'll undoubtedly change their strategy if it means that destruction of their party.