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Maybe just as impressive in a polarized political world is Mr. Paul’s ability to draw from all sides of the spectrum.

Walter E. Block, a professor at Loyola University in New Orleans and one of the speakers at Sunday’s rally, said that was evident from online discussion boards, where liberal blogs that usually treat Republicans’ ideas with disdain gave Mr. Paul a hearing.

That played out when looking at who supported Mr. Paul during the GOP primaries as well.

“Ron doesn’t do that well among Republican voters. He lost to the other guys, although he came in second here and there. But among the uncommitted, he did better than the others, and among Democrats, he did way better,” Mr. Block said.

‘Moneybomb’ pioneer

Analysts said Mr. Paul also has reshaped the way campaigns are run.

His “moneybomb” fundraisers — invented by his supporters and readily adopted by the campaign — have been copied by other candidates.

His use of GOP rules to maximize delegates won at state-level contests has Republican Party officials rethinking the way they set up the nominating primaries.

“He has signaled to the Republican Party leadership the peril of having caucuses versus primaries,” said Mr. Jones. “If Ron Paul has had an effect, he’s raised awareness within Republican Party circles of the liability associated with caucuses — that they’re much more difficult for the party elite to control.”

Beyond the people and the tactics, there are his stances that once seemed fringe views, but now approach party orthodoxy.

Four years after Mr. Paul called for shutting down entire Cabinet branches, in the 2012 primary season his fellow candidates competed to out-slash him — though in the end his pledge to cull five entire departments still bested the field.

In Congress, meanwhile, where Mr. Paul earned the monicker of “Dr. No” for his repeated votes against spending bills and much of the other annual legislation that props up the government, he has been joined by an entire corps of lawmakers willing to take those stands.

One of those is Rep. Paul Ryan of Wisconsin, whom Mr. Romney tapped this month to be his running mate.