From the Ryan Lizza New Yorker story:

“If it gets thrown to the House of Representatives and it goes beyond one ballot, I could be President,” Johnson said, smiling at the absurdity of the idea. “Because, if it goes beyond one ballot, Democrats are not going to cross over the line to change to Trump, and Republicans are not going to go over the line to support Clinton. They’re going to have to compromise, and I’d be the compromise.”

The 12th amendment provides that if no one gets a majority for President the House votes by state, and it is hard to imagine the Republican not chosen by the House.