“I’ve always maintained that I think the majority of the people in this country are libertarian — they just don’t know it,” he said. “Speaking with a broad-brush stroke, that’s being fiscally conservative and socially liberal. … I think most people fall in that category.”

Nicholas Sarwark, who chairs the Libertarian Party, is counting on those voters to finally tire of the choices the GOP and Democrats offer.

“The people who have been Republicans for decades and decades [and] true-blue establishment Republicans feel like they’ve been betrayed by a populist that has no moral center,” Mr. Sarwark said. “And on the Democratic side, the serious progressive activists who actually don’t want to have foreign wars and don’t want to keep locking people up for what they put in their bodies and want a more true progressive candidate are being betrayed by their party establishment.”

He said the interest in Libertarians is so high that former presidential candidates have sounded them out about joining seeking the party’s nod.