Nah, he should just bow out gracefully and not endorse the GOP sacrificial lamb who'll end getting slaughtered by Hillary. The GOP will use Paul's 3rd party run as an excuse to why they lost. This is where all of the 3rd party talk is coming from, GOP elitists. Hillary and Obama raised $100 million last year. There's no way in Hell the GOP can defeat Hillary. They don't have the numbers and the other candidates besides Paul and Romney are going broke. Better to just let the GOP learn the hard way. This is what happens when you abandon your principles.
If/when the GOP loses in November the only lesson they will take from it is that they didn’t moderate (read: shift leftward) enough.
There is nothing that will cause the GOP leadership to think the problem is that haven’t been conservative enough.
When Thompson bows out you can stick a fork in the GOP. It’ll be dead and the only thing left to do for conservatives is to bury it and start again.