Ron Paul wanted some legitimacy this time around, a bigger platform for his movement, and with his third-place showing in last night’s Iowa Republican Caucuses, he might just get it.

On stage before a cheering crowd in a hotel ballroom here as the final votes were being counted, Paul said that winning elections is the best way to promote a cause, declaring himself one of the night’s three winners.

Paul claimed a ticket out of Iowa, vowing to continue his fight, even as his GOP rivals have dismissed him as a fringe candidate and as party leaders have flatly declared him unelectable.

Iowa voters thought otherwise, taking to Paul’s strident antiwar and small-government message in enough numbers to lift him into a finish just a few percentage points behind Mitt Romney and Rick Santorum. Evangelicals, home-schoolers, young people, moderates, libertarians and disaffected Democrats formed an unlikely coalition that led to Paul’s strong showing, and at his Tuesday evening rally he predicted Iowa would be a launching pad to bigger things.

“We have tremendous opportunity to continue this momentum, it won’t be long that there’s going to be an election up in New Hampshire, and believe me, this momentum is going to continue and this movement is going to continue and we are going to keep scoring,” Paul said to his supporters. “So tonight, we have come out of an election where there were essentially three winners, three top vote-getters and we will go on, we will raise the money, I have no doubt about the volunteers.”

The question for Paul, though, is how he can capitalize on one good night in Iowa and turn it into more good nights in New Hampshire, South Carolina and beyond.

As returns came in Tuesday, he got something of a lift from former Alaska governor Sarah Palin, who said that the Republican Party should not ignore the Texas congressman’s view of fiscal policy or his fervent base of young supporters.

In New Hampshire, Paul has been airing a 60-second TV commercial that touts his consistency and casts him as the only candidate who can take on Washington. A campaign aide said that he will “make a real run at Mitt” in New Hampshire, a firewall for Romney, with a strong ground game and an aggressive ad campaign.

“He has an image problem among conservatives and Republicans on foreign policy, but his anti-Washington message is the strongest, and he has some great spots that are unique and that are breaking through,” said Michael Dennehy, a New Hampshire strategist who advised John McCain in 2008. “He will continue to pick up support in New Hampshire, especially from moderates and independents — but he does have a ceiling, of about 22 to 25 percent.”

On the stump, Paul has led with a strong antiwar message, vowing to shrink the military’s footprint and slash the defense budget.

Paul, who was a flight surgeon in the Air Force, says he has received more donations from active-duty military members than all of his rivals combined, some $112,000. His message of radically shrinking the size of government has especially resonated with young people — particularly men — and over the next days, the campaign will continue to deploy Paul’s son Rand, a Republican senator from Kentucky, as a top surrogate in New Hampshire and South Carolina.

South Carolina has a significant number of evangelicals, who caucused for Paul in Iowa and will probably be a crucial voting bloc in the Palmetto State’s Jan. 21 primary. To appeal to them, the Paul campaign recently started running an antiabortion ad in South Carolina highlighting the Texas congressman’s work as an obstetrician.

Less clear is how his foreign policy stance against military intervention will play out in a state with a sizable military population.

“People that haven’t heard from us yet and haven’t really heard what Ron really stands for on foreign policy, they have to scratch their heads a little bit,” said Jesse Benton, Paul’s national campaign manager. “Luckily we’ve got the resources and the volunteers to be able to communicate directly with the voters and let them know what Ron really stands for.”

In Iowa, at least, that strategy worked well enough for Paul to have doubled the votes he received in 2008, when he campaigned with much the same message.

“Dr. Paul isn’t going to change or tailor his message to fit any audience and that’s what people like about him. We are going to keep doing what we’ve been doing,” said Gary Howard, Paul’s press secretary. “We are in this for the long run.”