CHICAGO (CBS) — Mitt Romney won handily in the New Hampshire primary Tuesday, but his challengers say they are ready to fight in South Carolina.

Romney came in with 40 percent in New Hampshire, followed by 23 percent for Ron Paul and 17 percent for Jon Hunstman.

But political analyst Stephen Caliendo says Romney will likely encounter more difficulty in South Carolina, a state with an atmosphere is even more socially conservative than Iowa – where Romney came within eight votes of Rick Santorum.

“That eight votes in the Iowa Caucuses makes a big difference now, if you’re thinking about what the frame for this narrative is,” Caliendo said on the CBS 2 Morning News Wednesday. “South Carolina is going to be more of a challenge for social conservatives; a lot of social conservatives still in the contest.”

But if Romney does emerge victorious in South Carolina, it will be tough to beat him in Florida. That, in turn, would leave him 4-0 in the caucuses and primaries by the end of the month.

Regardless of whether their conservative values lies primarily in social issues or economics, many voters likely chose Romney as the candidate most likely to defeat President Barack Obama in November, Caliendo said. But many, he said, might have chosen other candidates, on the grounds that Romney might not so easily beat Obama after all.

“I think they’re thinking Mitt Romney’s in the 1 percent – he’s one of the folks who might be part of the problem, and it’s going to be very easy for the Obama administration to paint him that way,” Caliendo said.

Meanwhile, Huntsman said he would quit the race if he didn’t come in third in New Hampshire, but he did, indeed, end up coming in third. Caliendo says that was a big victory for Huntsman, but he, too, will encounter a struggle in South Carolina.

“These are folks who are very conservative with respect to social issues. He doesn’t have the same credentials as some of the other candidates, so it depends how much money he raises,” Caliendo said. “His third place finish this week will help him in raising money.”

Caliendo says if Romney wins in South Carolina, that doesn’t mean the primary is over.

‘One of the things that Ron Paul is going to be able to do, I think, with as much support as he has, is stay in maybe until the convention, which is important to him, because then he’ll be able to give an important convention speech,” he said, “and if the folks who are the libertarian part of the Republican Party want to take over and be an important voice within the Republican Party, that’s something that they’re going to be looking at for sure.”

More about Stephen Caliendo.