“I’m not sure he’s the optimal messenger,” said Charlie Cook, the political analyst.

But there is the Libertarian Party and then there is the libertarian  small-“L”  state of mind. Those who do not necessarily vote with the party but identify with some of the core libertarian philosophy  a small government with minimal reach into people’s personal lives, and minimal foreign entanglements  may be a potent, if unpredictable, group of voters.

“I think one problem the Republican Party is facing in the Mountain West is that the social, cultural and religious emphasis of Republicans in the last five, six, eight years has run against the libertarian grain,” Mr. Cook said. “When these people signed onto small government, they weren’t just talking about money. They were talking about small government, period. So when government dictates anything, whether social, cultural, religious or anything else, they take a dim view of that.”

Libertarians trace their historical roots back to the Enlightenment and views of the rights of the individual that informed the Constitution, which they say should be strictly interpreted. As might be expected from a group placing a high value on individual freedom, they are a diverse bunch, animated by different issues, whether gun rights or drug legalization or cutting taxes.

When libertarian ideas gained in popularity in the 1970s, it was in part from public discontent with big-government efforts like the Vietnam War. Lately, libertarians have focused on issues like the war in Iraq, which they oppose in common with many Democrats, and school choice, which they favor along with social conservatives.

Many view Mr. McCain, the presumptive Republican nominee, with suspicion if not disdain, despite his opposition to government pork, a maverick image and roots in Arizona, home of the Republican Senator Barry Goldwater (he of “extremism in the defense of liberty is no vice”). They oppose Mr. McCain’s support both of the war and campaign finance restrictions, which they see as a curb on free speech. Meanwhile, liberal Democrat though he may be, Senator Barack Obama, Mr. McCain’s likely foe, may attract libertarians not only because of his antiwar views but because, like Mr. Paul, he has had great success organizing support via the Internet, where a libertarian spirit thrives.

Mr. Boaz of the Cato Institute said he already detected some movement to Mr. Barr. “I’ve had friends e-mail me over the last few days and say, ‘I want Barr to keep McCain out of the White House,’ ” he said. “So there definitely are some libertarians who object to McCain and want to see Barr siphon votes away from him.”

Mr. Barr is expected to attract votes in libertarian strongholds like Colorado, Idaho, New Mexico and New Hampshire. One recent poll suggested that Mr. Barr could do the most serious damage in his native Georgia, where Mr. Obama, with his wide support among black voters, could perform well, too.