Is there any example of someone running for an unpopular incumbent party and winning by running against it? I know that's how Sazkozy won but that was France.
As was already mentioned, Bryan won the 1896 nomination, although not the general. The Democratic party had lost over half their seats in the House in 1894.
There is also 1856, which was equivalent to a successful primary challenge to an incumbent president in the modern system, with the primary challenger going on to win the general election for the incumbent's party.
And that President basically destroyed the country and is the closest thing we have to an example for Schweitzer to follow. It would basically be unprecedented in American history for him to be successful, then. I like Schweitzer but that doesn't mean that I don't like Obama or Clinton, too though they are very different.