What would a third party presidency actually look like?

[kyc0705]

Let's imagine some fantasy world in which a candidate who is not a Democrat or a Republican is elected President. What would actually happen in their administration? Would a third party president have a chance of getting re-elected?

For the sake of argument, let's use Gary Johnson. One would presume that a few Libertarians would find themselves in Congress off the coattails of his victory, but they wouldn't be anywhere near a majority. Would Democratic and Republican leaders be able to work with him since he wasn't from the other party, or would they find a common enemy in him? What would his cabinet look like? All Libertarians or more than a few concessions?