COLUMBIA - South Carolina Gov. Nikki Haley has a slim lead over her Democratic opponent and a wide margin over two other challengers in a state that is deeply divided over the incumbent governor's leadership, a Palmetto Politics Poll shows.

About Palmetto Politics Poll

A poll of 1,000 potential voters was commissioned by The Post and Courier, WCIV ABC News 4 (Charleston), WYFF News 4 (Greenville) and WACHFOX (Columbia). Margin of error plus/minus 4 percent.

The poll of likely voters commissioned by The Post and Courier and three television stations shows that in a matchup with Democrat Vincent Sheheen, Haley leads Sheheen by four percentage points - within the poll's 4 percent margin of error. Haley led overall with 46 percent support of those polled among the 650 likely voters surveyed.

In the matchup, Sheheen garnered 42 percent, independent Tom Ervin 3 percent and Libertarian Steve French 2 percent. Six percent of voters polled were undecided about the race, which features a 2010 rematch of Haley and Sheheen.

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In a separate question posed to 1,000 potential voters, Haley would have a double-digit lead over Sheheen if he were the only other candidate in the race, with the incumbent leading 53 percent to Sheheen's 40 percent in their head-to-head race.

The poll underscores the role that third-party challengers Ervin and French could play in the race, said pollster Jim Lee, president of Pennsylvania-based Susquehanna Polling and Research, which conducted the survey.

"It has the potential to be really close," Lee said of the race.

But Lee said a deeper dive into the numbers suggests a difficult road for Sheheen, a state senator from Camden. Those polled ranked health care and job creation as the state's top issues, with education not far behind.

That suggests that it will be difficult for Sheheen to hone in on one issue to siphon voters from Haley, Lee said. Couple that with the fact that Republicans tend to vote more in nonpresidential elections, the race is Haley's to lose, Lee said. He also said that while some potential voters tell pollsters they would vote for a third-party candidate, many get to the voting booth and decide otherwise.

"Barring something fundamentally changing the narrative ... this looks to me like a Haley victory this November," Lee said.

College of Charleston Political Science Professor Gibbs Knotts said he would expect Haley to do well as the incumbent, given the improved economy. As for French and Ervin's numbers, Knotts said it's difficult for candidates of other parties to win.

"It certainly happens, but it doesn't happen a lot," Knotts said. "But they can impact the election and impact election results by hurting one candidate or the other."

One change, Lee said, could be a successful challenge from French, a Charleston Libertarian, or Ervin, a former judge and S.C. House member. The numbers show that both candidates pulled potential voters away from Haley, among those polled.

Knotts believed, however, that as an incumbent, Haley has more of a cushion to take a hit from straggling voters.

Still, the close margin despite a wide gulf in fundraising should give Sheheen's supporters much to cheer about, experts said. The poll shows that Republicans generally approve of Haley's leadership and Democrats do not. In all, 48 percent of those polled approved of Haley's job performance, while 41 percent disapproved. Eleven percent of voters were undecided on that question.

Knotts said Haley's approval number was "a little low" for an incumbent governor in a state that's predominately Republican.

The last time a Democrat won the governor's office was when Jim Hodges was elected in November 1998.

"I personally expect a Republican incumbent with a rebounding economy to have a little bit higher approval rating," Knotts said. "It does show that she does have some vulnerability. But again, in this particular state, it is certainly an uphill battle for Sheheen."

Neal Thigpen, a former politics professor and longtime South Carolina politics watcher, said the poll was good news for Sheheen supporters. It also shows that early Republican Governors Association advertisements that criticized his work as a defense attorney did little damage, he said.

"Vince's problem is the money," Thigpen said. The RGA, which seeks to elect Republicans across the country, has outraised its Democratic counterpart two-to-one, and Haley had a record fundraising effort last quarter, more than doubling Sheheen's quarterly campaign fundraising effort.

The election is Nov. 4.