Any Republican nominee has a shot at winning a state that Romney lost by under eight points, and that has consistently been between 2-6 points more liberal than the rest of the country in presidential elections.
It's the state of Jesse Ventura and Justin Amash although the independent streak may not be that important. Ventura's election was in 1998, and he got 37% (although he and Coleman did have a combined 71%.)
Justin Amash? Of Michigan?
Also, electing Jesse Ventura in 1998 does not make it a libertarian state. Minnesota is a solidly liberal state and, as far as I can see, will continue to be in the near future. While its election results have not been the most convincing, it's the lack of elasticity it has shown in presidential elections that give me reason to believe Rand Paul and his politics would do poorly unless stacked against an utterly terrible Democratic candidate.