Earlier quoted context omitted.
One of the few concrete functions of the Vice President once elected, is to serve as a more extreme alternative to the political positions of the President. That way, nobody opposed to the President's platform can assassinate the President in the hopes of killing that platform, because it will only be replaced with a worse version. This is not the case in an across-the-aisle Presidency. There are lots of Paul support…
The broader problem is that the Vice President has no real power. You can't balance a Presidency with an across-the-aisle candidate because the Vice President can't meaningfully do anything without the President's assent. The interesting thing is if the Democrats nominate Sanders and the Republicans nominate Paul.
Interesting, if only due to its impossibility.