WASHINGTON — Ron Paul's strong early showing in the race for the Republican presidential nomination could leave rivals with a fateful choice: Tilt toward his views or risk an election-changing third party bid.

After coming third in Iowa and second in New Hampshire -- the first votes to choose the Republican who will challenge President Barack Obama in November -- the unorthodox 76-year-old has shot unexpectedly into the mainstream.

Yet there is still an overwhelming sense that Paul is in the Grand Old Party, but not of the Grand Old Party.

"He is using the Republican process to run for president, but I wouldn't talk about him in terms of being a Republican party candidate," said Terry Holt a veteran of George W. Bush's presidential campaigns.

"He is a Republican because he is running in a Republican primary, but he is a libertarian, those are his political roots."

It is a truism that Paul's support for legalizing drugs, decimating military spending, cutting aid to Israel, ignoring Iran's nuclear program and abolishing the Federal Reserve are anathema to most Republicans.

But Paul's electoral performance has given him, and his sometimes controversial views, enough political clout to be respected and taken seriously.

"If Republicans don't understand the important aspects of what Ron Paul is saying, I don't think we will continue to exist as a party, certainly not as a majority party," South Carolina Senator and Tea Party favorite Jim DeMint told Fox News on Thursday.

"Some of the foreign policy I can't go with, but... the unaccountable and out of control Federal Reserve, individual liberty, the constitutional limited government, those are the concepts that Ron Paul is bringing forward and all of our country needs to listen to that."

There are very practical reasons why Mitt Romney, Rick Santorum, Newt Gingrich and other Republican candidates would want to court Paul's voters.

According to New Hampshire exit polls, Paul was the first choice among voters aged 18-29, those earning less than $50,000 a year, first time GOP voters, independents and those looking for a "true conservative."

Few believe than Paul can parlay that support into enough delegates to win the nomination, but party elders are careful not to trample his ideas in case he bolts from the party altogether.

In 1988, the GOP fretted little about Paul's third party bid for the presidency, but given his current success a third-party run could completely recast this year's election.

The specter of Al Gore's loss in the 2000 election to George W. Bush -- often attributed to the third party candidacy of Ralph Nader -- hangs thick in the air.

"It would add a problematic dimension to the overall popular vote," said Holt.

How to keep Paul and his supporters inside the tent is a problem now vexing party elders.

"The thing about Ron Paul is, what does he want that we have?" Holt asked. "He has never been someone who was interested in being co-opted or in trading and dealing."

"When I was a staffer in the Republican leadership in the House (of Representatives), whenever we were trying to find votes for whatever we were doing, he would tell us how he was voting and that was that.

"There was nothing he wanted that we could offer him in exchange for his vote."

Already there are mutterings about giving Paul prime speaking time at the GOP convention in September -- the largest political stage yet for his ideas.

But if his strong showing continues in the upcoming primaries in Florida, South Carolina and beyond, Republicans might have to think harder about how they solve the problem of Ron Paul's rise.