The Harper Polling survey found Capito leading each possible Democratic challenger by double digits. The poll found Capito leading Rep. Nick RahallNick RahallLikely W.Va. Senate GOP rivals spar in radio appearances West Virginia is no longer Clinton country Solution needed: Rail congestion is stifling economic growth MORE (D-W.Va.) 50 percent to 31 percent with about 18 percent saying they are not sure. In a matchup between Capito and former Sen. Carte Goodwin (D-W.Va.), Capito leads 53 percent to 19 percent with 27 percent saying they aren't sure. The Harper Polling survey also found Capito with a wide lead against West Virginia State Supreme Court of Appeals Justice Robin Davis (D), 51 percent to 24 percent with about 24 percent saying they are unsure.

Both Davis and Rahall have suggested they are interested in running for Rockefeller's seat but neither of them have formally jumped into the race. Goodwin hasn't indicated whether he plans to run or stay out of the race.

Rep. David McKinleyDavid Bennett McKinleyLawmakers slam DOE’s proposal to help coal, nuclear power Lawmakers try again on miners’ pension bill There’s a way to protect consumers and keep good call center jobs in the U.S. MORE (R-W.Va.), who's name has also been floated as a possible candidate for the race, has also indicated that he will likely back Capito's bid, according to West Virginia's The Intelligencer and Wheeling News-Register.

"I have told Shelley I am keeping my options open. I really think at the end of the day we'll be supporting Shelley," McKinley said according to the Intelligencer and News-Register.

The survey had a sample size of 1,444 people and was conducted Jan. 21. The margin of error was plus or minus 2.58 percentage points. Harper Polling is run by Brock McCreary who previously served as the National Republican Congressional Committee's pollster.