For almost 95 years, the dominant question facing any North Carolinian has been over shades of blue: Duke or UNC.

But in the final months before May’s Republican primary to select a challenger to Democratic Sen. Kay Hagan, the debate among Tar Heel Republicans has focused on shades of red — specifically, just how conservative their nominee and state should be.

Hagan’s seat marks a prime pickup opportunity for Senate Republicans, who must net six seats in November to win the majority. Recent automated polls have shown a tight race: Hagan’s GOP opponents are ahead by a couple points, and their leads almost always fall within the margin of error.

Though Mitt Romney won the state by a narrow margin in 2012, the Republicans easily regained the governor’s mansion just two years after sweeping the legislature, giving the GOP total control of the state government for the first time since the late 1800s.

So as plum as November seems for the GOP, this spring and summer are shaping up to be a political free-for-all, with several anti-establishment candidates bidding to force state Speaker Thom Tillis from a May 6 primary into a July runoff.

“Our goal, our job, is to get in the runoff,” said Republican consultant Tom Perdue, who is working for Mark Harris, a Mike Huckabee-endorsed, conservative Baptist pastor. “When we say we think we can win, that’s all we’re saying, is we think we can get into the runoff.”

Perdue, a Georgia-based consultant who was once retiring Sen. Saxby Chambliss’ top political operative, said he joined the Harris campaign because he believed there was a window for a true conservative against the “slick,” “establishment” Tillis.

“There is no hands-down front-runner,” Perdue said. “If he were going to have been the hands-down winner, he would have had most of the House members supporting him by now … if he were really going to be the hands-down winner, he would have raised a lot more money last year. And if he were going to be the front-runner, you wouldn’t see six or seven people jumping into this race.”

Harris and Greg Brannon, a physician, are the two most viable primary challengers to Tillis, according to a half-dozen state-based sources, including some unaffiliated with any of the campaigns. However, Brannon hit a significant bump in the road Tuesday, when a Wake County jury found him liable for misleading investors in a civil suit.

None of the GOP candidates enjoy high levels of name recognition or fundraising. According to the most recent Federal Election Commission data, Brannon had $142,329 in cash on hand and Harris had $255,800 at the end of last year. Tillis reported having almost $1.3 million in the bank.

Hagan’s campaign toppled all of those numbers combined with nearly $7 million in cash on hand at the end of 2013.

Conservatives face another problem: There’s no consensus candidate. Sources pointed to the fact that North Carolina has no centralized tea party organization. Former Arkansas Gov. Mike Huckabee endorsed Harris, while Sen. Rand Paul, R-Ky., backed Brannon in October.

The key to a Tillis victory, per operatives inside and outside his campaign, is demonstrating that even though he may be a favorite of the party’s most-established members, he is also conservative.

The state house Tillis oversaw was one of the most conservative in decades: Republicans restructured the tax code, approved new voter identification law, got an anti-gay-marriage provision on the statewide ballot (which passed), and enacted teacher pay cuts.

“This primary is about a record of achieving conservative results that Thom Tillis can point to, but it’s also about understanding the fact that the path to a Republican majority in the Senate runs through North Carolina,” said Tillis spokesman Jordan Shaw. “We’re focused on beating Kay Hagan in November. … We’ve got a lot of work ahead of us, but we’re confident with where we are.”

Many Republican operatives believe Tillis will have the resources to emerge from the primary successfully. But sources also warned a runoff remains probable, and if tea party factions coalesce around one candidate, that potential second GOP contest would be a more intense challenge.

Hagan won her first term in 2008 with an 8-point margin of victory over Republican Sen. Elizabeth Dole. Hagan’s re-election is rated Tilts Democrat by Rothenberg Political Report/Roll Call.