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William A. Galston of the Brookings Institution said Republicans are wrestling over the future of the party in the same way that they did more than six decades ago when supporters of isolationist Sen. Robert Taft of Ohio clashed with supporters of retired Gen. Dwight D. Eisenhower over foreign policy before the 1952 presidential election won by Eisenhower.

Rand Paul’s brand of libertarianism is reminiscent of Taft, and the debate over Syria offers him a golden opportunity to articulate his governing philosophy before a national audience,” Mr. Galston wrote Tuesday.

Nick Gillespie, editor in chief of Reason.com, the largest libertarian news website, said the debate gives the libertarian wing of the party a chance to question the foreign policy that started under Mr. Bush and continued under Mr. Obama.

“The intra-GOP rift over Syria showcases the growing power of the libertarian wing of the Republican Party and its ability to tap deeply into public opinion in a way that neither mainstream Democrats or hawkish Republicans can,” Mr. Gillespie said, complimenting Mr. Paul and Mr. Amash for their opposition to intervention. “The libertarian wing of the Republican Party will come out of this stronger and more in touch with the vox populi.”