One way to measure Rep. Ron Paul’s ascendance as a political player is to compare the cold shoulder he got from rival Republican presidential candidate John McCain in 2008 with the cozier embrace he has received from 2012 presumptive nominee Mitt Romney.

When Mr. Romney announced Monday that he supports auditing the Federal Reserve, it underscored the odd but powerful influence of the maverick congressman from Texas, whose years-long push for a Fed audit will now appear in the party platform.

From overseas adventurism to deficit spending to a distrust of government institutions, the gospel of Paul has revived long-simmering debates that were muffled during the eight-year tenure of President George W. Bush — and, at least on some of those issues, Mr. Paul’s side appears to have gained the upper hand.

Indeed, with Mr. Paul and his ardent supporters set to play a visible role in the Republican National Convention next week in Tampa, Fla., it’s arguable that Mr. Paul, in his 2008 and 2012 presidential campaigns, has done more to shape the party’s ideology than either Mr. McCain or Mr. Romney.

“More than anything else, what Ron Paul with these past two presidential runs has done is used the Republican Party presidential process as a platform to proselytize to an audience that otherwise wouldn’t hear it,” said Mark P. Jones, chairman of the political science department at Rice University in Houston, just north of Mr. Paul’s southeast Texas congressional district.

Final bow

This weekend, Mr. Paul will walk onto — then off of — the political stage, literally and figuratively.

His campaign has scheduled what it is billing as the “We Are the Future Rally,” to be held Sunday at the University of South Florida’s 10,000-seat Sun Dome. Mr. Paul, in an email to supporters this month, promised his address would be the “speech the Republican National Convention doesn’t want the rest of America to hear.”

He is retiring from Congress and, despite the fervent arguments of his supporters, he is unlikely to win the Republican Party’s nomination next week.

So what happens next?

Most analysts are looking to Mr. Paul’s son, freshman Sen. Rand Paul of Kentucky, who campaigned heavily for his father during the presidential primary season. But the younger Mr. Paul endorsed Mr. Romney once it became clear that his father couldn’t win — a move that angered some of his father’s supporters.

The son has been given a prime-time speaking slot at the convention Monday that observers said was a way of giving a nod to Ron Paul without having him officially speak.

Meanwhile, Gary E. Johnson, the former New Mexico governor who left the GOP to become the Libertarian Party’s presidential nominee this year, has pleaded with Paul supporters to give him a look-see.

“Just like the Republican establishment who tried to silence Congressman Ron Paul, the powers-that-be are determined to keep the American people from hearing, seeing or even having a chance to vote for Gov. Gary Johnson,” Ron Nielson, Mr. Johnson’s senior campaign adviser, said in an email this week to rally support. “They’re afraid. They know millions of Americans, if given a chance, will reject the big-government candidates and join the liberty movement.”

For Republicans, the question of what Mr. Paul’s followers do is more pressing. Without their backing, Mr. Romney could have a tougher time carrying key swing states such as New Hampshire and Colorado.

Those followers aren’t in the best of moods. Many think Mr. Romney played dirty by trying to deny Mr. Paul more delegates and a speaking slot at the convention, and Paul-oriented message boards have been burning up with debate about how to respond.

“No more deals with devils,” one commenter wrote on DailyPaul.com.

But another shot back: “Leaving now, and giving up the voting positions you have in the GOP and everything else you have gained these few years, is quitting and very foolish.”

The prophet

Given that level of debate within the Paul movement, it’s amazing that someone was able to keep them all on the same page for so long.

That has been Mr. Paul’s chief accomplishment. Though the physician and 12-term lawmaker was not particularly effective in winning voters during the Republican primaries, he used the party’s own rules to build a cadre of dedicated delegates whose influence will reverberate within the GOP for years.

Many of those followers say they weren’t politically active until they came across Mr. Paul and his message, particularly his thoughts on monetary policy. YouTube clips of his confrontations with Fed Chairman Ben S. Bernanke have drawn hundreds of thousands of views.

For many, he is their political prophet.

“In the same way that somebody steps into a church and makes a decision of faith, and that’s the preacher they were converted under, they’re going to stay under him until some disillusion sets in or maybe they’ll widen their intellectual background or they grow up in the faith, and they learn from themselves,” said Mark Edward Taylor, author of the book “Branding Obamessiah,” which dissects Barack Obama’s winning 2008 campaign.

Visually, Mr. Paul does not cut the image of a political movement leader. But then, given who his supporters are, that probably works in his favor.

“His persona is the anti-politician. That was his look,” said Mr. Taylor. “The suits were baggy, the laugh was goofy, his voice quivered, but he was kind of the grandfatherly type you could trust. He was Ronald Reagan with some sharp teeth. He was really kind of more saintly than a slick politician, and that really, I think, carried the trust of his true believers.”

Those fans are, if nothing else, loyal to a fault.

CafePress.com, an online merchandiser that sells just about every piece of political paraphernalia imaginable, said Paul items dominated the Republican field in the early going, even as other GOP candidates rose and fell. In fact, in January, Mr. Paul’s gear outsold Mr. Romney’s by better than 3-to-1, and was within striking distance of sales of Obama merchandise.

It wasn’t until June — well after the GOP contest was essentially over — that Mr. Paul fell back to earth.

“Ron Paul has a very different effect on sales and, ultimately, votes than we’ve seen,” said Marc Cowlin, director of marketing at CafePress. “It’s interesting to watch. The people who are interested in Ron Paul tend to consistently come back, want to hear what he has to say, and consistently buy merchandise.”

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.

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