COLUMBIA, S.C. -- While voters in South Carolina frequently tout their independence from those in Iowa and New Hampshire, that doesn’t mean they ignore the results of those states’ primary contests.

No candidate since 1980 has won South Carolina without first winning one of the two earlier states, and interviews with voters before Tuesday’s caucus, and follow-ups the next day, suggested that Iowa’s outcome -- a razor-thin margin between Mitt Romney and Rick Santorum, and low tallies for several other candidates – was not ignored in the Palmetto State.

Before Tuesday’s vote, Denise Ward, a 44-year-old office manager at a Columbia elementary school, said she thought the Republican field looked like a “big, murky pond,” although she said she had narrowed her sights down to Romney and Newt Gingrich, never mentioning Santorum.

The day after the vote, however, Ward said the former Pennsylvania senator’s photo finish with Romney gave her “a moment to pause and think, ‘whoa, I’ve got a lot of thinking to do.’” That bears out in polling today when Santorum went from just 4% a month ago in a CNN/Time/Opinion Research poll to 19% and second place today. 

And while she didn’t seem quite ready to give up on Gingrich, she expressed concern that the former House speaker might not be able to revive his campaign before he comes to South Carolina.

“I don’t think it looks good for him if he doesn’t do well in Iowa and New Hampshire,” she said. (Gingrich took a nosedive in the poll out today, going from a commanding 43% and first place to third and 18%.)

The candidate expected to do well in the Granite State – Romney – was given favorable, albeit begrudging, consideration by several other South Carolinians the evening before the caucus. 

“I dislike them all, but I’m going to vote, so I’m going to have to pick one,” said Eddie Bagwell, a 77-year-old retired barber from the Upstate Greenville County. After the caucus, Bagwell said he was “bordering on Mitt Romney,” because “the object of the game is to put a candidate in office that will beat the Democrats.”

Bagwell added that Romney’s Mormon faith was not a deal-breaker for him. “They’ve got a pretty strict  doctrine,” he said of the LDS faith. “As a Baptist, I’ve heard some people complain about it, but personally, I don’t see anything wrong with it.”

Romney saw a big boost in the CNN/Time poll. He now sits in first place with 37%, up from 20% a month ago.

Carolyn Lindler, a 71-year-old retiree from Newberry County in the state’s Midlands, was also lukewarm toward Romney, saying she preferred Gingrich but doubted his general-election prospects.  

“No. 1 for me would be Gingrich, but I will vote for Romney,” she said on Monday, before the Iowa caucus.

Lindler's hesitation on Gingrich was further solidified after the results came in early Wednesday morning. “I was at least hoping Newt would come in second,” she said, referring to Gingrich's fourth-place finish in Iowa, in a follow up interview with First Read.

Lindler also said she liked Santorum, but “he’s got too much pork,” she said, referring to his support of earmarks during his congressional tenure.  

While Lindler said she’d still likely vote for Romney, she was dismayed at what she characterized as a choice between the most electable candidate and the best potential president.

“I see more people voting not for who they think is the best man, but for who the best man is to beat Obama,” she said. “And that’s really sad, but it’s the situation that we’ve caught ourselves up in.”

But another Gingrich supporter, James Blaine, a 58-year-old truck driver from Berkeley County, in the southern part of the state, said he wasn’t ready to give up on his preferred candidate. An Iowa native, Blaine said of the caucus results, “My Iowans let me down.”

Dennis Stratton, a retiree from Lexington County, also said he would base his vote only on personal preference. A Rick Perry supporter, who said he liked the Texas governor’s military service, Stratton also voted for Mike Huckabee in 2008. Huckabee won Iowa, but finished second in South Carolina.

“I want to throw my hat in the ring for the person I like the best," he said, "and I think every American ought to do that."

Stratton also said he wasn’t swayed by Sen. John McCain’s endorsement of Romney (the two campaigned together in Charleston today) -- despite McCain's war-hero credentials. “It’s one moderate endorsing another one that tends to be a little more moderate,” he said.

Not all voters woke up disappointed by Wednesday’s results. Billy Chasteen, a 72-year-old retiree from the Midlands’ Calhoun County, said he was glad to see Rick Santorum, his preferred candidate before the caucus, come in virtually tied with Romney.

“Right now he’s still my man,” Chasteen said, adding, however, that he was unsure of the negative attacks Santorum’s opponents have in their arsenal. “I don’t know anything on him yet. It’s going to get bad before it gets better.”

Chasteen also said that Santorum’s Catholicism, in a state where only a small minority practices the religion, was not an issue for him. “I have a lot of Catholic friends," he joked. "They just believe different from what I do. Maybe we can get him converted!”