A new Winthrop University poll finds Texas Gov. Rick Perry holding a lead on former Massachusetts Gov. Mitt Romney among South Carolina Republicans.

But the gap is narrowing.

The results, released Tuesday, show that of respondents who said that they definitely planned to vote in South Carolina's presidential primary, 30.5 percent favored Perry and 27.3 percent supported Romney.

"The race right now is wide open," South Carolina GOP executive director Matt Moore said. "Republicans expect the candidates to come here and campaign hard and convince them."

Minnesota Congresswoman Michele Bachmann's popularity among those same Republicans is falling, according to the poll, while businessman Herman Cain is gaining some ground on the field. Eleven percent of participants said they were still undecided.

In a similar poll conducted during late August, Perry held an 11-point lead over Romney.

Moore said the narrowing gap likely reflected the nature of polls this early in the race rather than mistakes by Perry or improvements by Romney.

"It's extremely early," Moore said. "There's a long way to go and these candidates have to make the final pitch to close the deal."

The poll also found that 35.4 percent of those planning to vote in the primary expect Perry to win, while 29.4 percent expect Romney to win.

Among the Republicans surveyed, 67.8 percent said they did not consider themselves Tea Party members, but 74.4 percent said they generally agreed with Tea Party principles.

Responders also said it was more important to select a Republican candidate who matched their political beliefs rather than focusing on someone who they felt could beat President Obama during the general election.

The poll also showcased S.C. Republican voters thoughts about Obama's policies, birthplace and religion, as well as support of S.C. Gov. Nikki Haley.