Republicans vying to take on incumbent U.S. Sen. Kay Hagan in North Carolina find themselves in a pitched battle with less than a month remaining before their May 6 primary … and the outcome of the race could upset some conventional wisdom about what sort of GOP candidate is best equipped to take on a vulnerable Democrat.

Thom Tillis – Speaker of the N.C. House of Representatives – has the support of 18 percent of the Republican electorate according to a recent Public Policy Polling survey. Physician Greg Brannon came in second in that survey at 15 percent, ahead of Charlotte pastor Mark Harris (11 percent) and nurse practitioner Heather Grant (7 percent).

“The Republican primary race is still pretty wide open with less than a month to go until the election,” said Dean Debnam, President of Public Policy Polling. “Thom Tillis just hasn’t been able to break away from the pack.”

Tillis is the choice of the GOP establishment – and is backed by Karl Rove and his organization. Meanwhile Brannon is the top choice of the limited government wing of the party, receiving the support of groups like Freedomworks.

Hagan’s approval rating is languishing at 41 percent (compared to the 48 percent of Tar Heel state voters who disapprove of the job she’s doing). In other word’s she’s ripe for the picking – unless of course the GOP establishment forces its candidate of choice into the general election.

According to the PPP survey, Tillis is the only “Republican” currently trailing Hagan in a general election matchup – by a 43-41 percent margin. All of the other candidates enjoy slight leads over the incumbent.

Interesting … so in North Carolina, it would appear the GOP establishment’s old “electability” argument is working against the establishment choice.

PPP’s latest North Carolina poll surveyed 740 registered voters (and 314 “Republicans”) from April 3-6. Its margin of error is plus or minus 3.6 percent overall and 5.5 percent for GOP voters.