While Senator Paul and Mr. Amash alienate some Republicans, libertarian stands against policies like the bailouts and the federal drug war have potential crossover appeal for Democrats and independents. “If we are ever going to win in California again, or Washington, we need someone who is a libertarian Republican,” Senator Paul told me.

The party that nominated Mr. Romney, and that gave only 16 Senate votes in May 2012 to Rand Paul’s five-year path to a balanced budget, might not agree. The consistency of the libertarian philosophy — roughly, that government exists only to protect citizens’ lives and property from assault — leads them to buck party discipline on spending. Senator Paul was among the few Senate Republicans who voted against the fiscal cliff deal. It also leads them to oppose civil liberties encroachments like the Patriot Act and the indefinite detention provisions of the National Defense Authorization Act and to condemn “crony capitalism” as exemplified by the Troubled Asset Relief Program and other government bailouts they see as illegitimately serving Wall Street and banking interests.

Mr. Amash is sure that libertarian consistency helps him, and could help the Republican Party. “It gives you credibility with people who might be mistrustful because you are Republican,” he told me. “It shows you are serious about following the Constitution and defending American people’s liberties.”

Ron Paul understood his mission as educational, not just political. He thought more Americans needed to be taught the economic and ethical benefits of a government that pretty much leaves us alone. His successors optimistically think Americans will embrace their libertarianism; more important, they are sure Americans need to, to avoid a fiscal and debt crisis they fear intensely.