DAVIDSON, N.C. -- The top four Republican candidates for Senate in North Carolina diverged only moderately on policy when they met onstage for a televised debate Tuesday.

But there was profound disagreement among them over who could best represent the party, and prove most electable, against Sen. Kay Hagan, the Democratic incumbent, later this year in a race that could tip the power balance in the Senate.

"Only one of us at this table, in the latest statewide poll, beats Kay Hagan outside the margin of error," argued Mark Harris, a baptist pastor who has appealed to the religious right. "And that is Mark Harris."

North Carolina Republicans are still well split among their party's hopefuls, polls show, and the debate at Davidson College, the first of two this week for those jockeying for the GOP nomination, laid bare some of the most basic fault lines in the Republican Party's framework of support. Social conservatism, libertarianism, and the so-called Republican "establishment" were all represented among the candidates on the auditorium stage: Harris; North Carolina House Speaker Thom Tillis; Dr. Greg Brannon; and Heather Grant, a first-time candidate and former military nurse.

Tillis, the Republican frontrunner who has received undisguised support from the national GOP and from influential pro-Republican outside groups hoping to avoid a costly primary, remained focused throughout the debate on staying above the Republican fray, instead attacking Hagan on a range of policies.

But Tillis failed to shy from a tense, stark disagreement with Brannon, a physician who skews Libertarian, roughly 45 minutes into the debate, on the issue of gun laws.

Brannon, citing the Second Amendment, said gun ownership should not be limited by the federal government. Tillis, noting his endorsement by the NRA, called that strict reading of the Constitution "irresponsible," and suggested convicted felons and the mentally ill should not be allowed to own guns.

"You can’t put a gun in the hands of someone who represents a danger to themselves and a danger to society," Tillis said. "Folks, this is being practical. This is being practical conservatives."

That frank assessment marked a notable swerve to the middle for Tillis, who has taken pains to highlight his conservative bona fides as he has sought to win enough support from primary voters to avoid a run-off against one of his Republican opponents.

If no candidate takes 40 percent of the vote during the primary election on May 6, the top two candidates will compete in a run-off election in mid-July.

In recent surveys released publicly, Tillis has struggled to come within striking distance of that threshold. In one poll commissioned by American Crossroads, a third-party group supportive of Tillis, Tillis won support from 27 percent of respondents.

Sending Tillis into a two-month-long, head-to-head match-up with either Brannon or Harris is been precisely the outcome Democrats have been hoping to force. Democratic third-party groups and Hagan's campaign have alternately attacked Tillis for being too conservative or not conservative enough, playing at once to all possible electoral ends.

To counter the latter line of attack, Tillis threw out plenty of red meat Tuesday for conservative supporters -- rejecting climate change as scientific fact, suggesting that the federal minimum wage be abolished, and roundly criticizing Obamacare.

"I'm one of the anti-establishment people," Tillis told reporters after the debate. "I've been busting up establishments for the last seven years in Raleigh, and I'm going to do the same thing in Washington."

Harris, in another huddle a few steps from Tillis, was meanwhile making the opposite argument.

"There's a lot of unhappy people in North Carolina with Thom Tillis and this legislature," Harris said.

Still, as all of the candidates were seated together onstage, when asked whether they would support whoever won the GOP nomination, each one in turn answered, "Yes."

The four candidates will debate again Wednesday during a televised event in Raleigh.

This story was first published at 2:08 a.m.