Speaker of the North Carolina House of Representatives Thom Tillis is running to unseat Sen. Kay Hagan (D-N.C.). (Brad Coville/AP)

Voters in North Carolina can be forgiven if they turn off their televisions. In the battle for control of the U.S. Senate, no state has experienced an onslaught of negative advertising as intense as what has been unleashed in the Tar Heel State.

The barrage is being fueled by wealthy independent groups from both ends of the political spectrum and reflects the importance that both parties place on winning the seat held by freshman Democrat Kay Hagan.

For more than a year, conservative groups have blanketed radio and television with advertisements assaulting Hagan. Americans for Prosperity, which is closely linked to the wealthy libertarian Koch brothers, has spent more than $7.2 million to highlight what it considers the negative aspects of Hagan’s record.

But after two consecutive elections in which ultra-conservative outsiders won Republican primaries and subsequently lost otherwise winnable general elections, GOP strategists in Washington, once loath to bestow the often-unhelpful “establishment” label on a favored candidate, are increasingly and openly aiding candidates they think have the best chance to win in November.

Republicans need to pick up six seats to take control of the Senate. The party’s candidates lead in two states where Democratic incumbents will retire, West Virginia and South Dakota, and lead or are running close to Democratic incumbents in Alaska, Arkansas, Louisiana and Montana, all states where President Obama is deeply unpopular. In the most hopeful GOP scenarios, North Carolina is the majority-clinching 51st or the breathing-room 52nd seat, and that means it is worth spending money and exerting influence to pick the right candidate.

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To many Republicans inside and outside North Carolina, that candidate is state House Speaker Thom Tillis, who national party strategists say is the only candidate who can beat Hagan in the fall.

“For the Republicans to have a real chance of picking the seat up, Tillis needs to win the primary,” said Brian Nick, a Charlotte-based GOP strategist close to Gov. Pat McCrory (R).

On Tuesday, American Crossroads, a Republican group spearheaded by Karl Rove, will begin running a television advertisement backing Tillis. The ad is part of a $1.1 million television blitz that will run through the primary election, on May 6.

“It’s clear to us that Thom Tillis has the experience, conservative principles and passion to clean up the mess that President Obama and Sen. Hagan are making in Washington,” Steven Law, the president of American Crossroads, said in a statement.

Tillis has emerged as the front-runner in a primary contest in which most voters haven’t formed an opinion. What little public polling exists shows Tillis leading physician Greg Brannon and Baptist minister Mark Harris, both of whom are portraying themselves as more conservative than Tillis, along with a handful of candidates who are less known, by double digits. But those polls show Tillis is short of the 40 percent of the vote he would need to avoid a runoff.

National Republicans are desperate to avoid a runoff, which would sap campaign accounts and allow conservatives who have tried to coalesce around a Tillis alternative the opportunity to do so.

In recent weeks, seemingly cementing the notion of Tillis as a front-runner with the clock winding down, Brannon and Harris have increased their attacks on the speaker.

Brannon has accused Tillis of fostering a “culture of corruption” that would make Tillis “unelectable” in November, highlighting two former staff members who received severance payments after being caught in sex scandals.

In states such as Colorado, Missouri and Nevada in recent years, Democrats have used competitive Republican primaries to quietly aid the most conservative, and hence least electable, candidates. But that isn’t an option in North Carolina; observers say neither Harris nor Brannon has the campaign cash or the grass-roots backing to seriously challenge the front-runner.

“There will be millions of dollars’ worth of Republican money coming in if Tillis is the nominee,” state Sen. Bob Rucho (R) said in an interview. “The money will follow Tillis. It won’t necessarily follow the other candidates.”

Tillis has been advertising on statewide cable channels since January and intermittently on low-cost broadcast networks in Asheville, Greensboro and Wilmington.

The actions of Hagan’s campaign and her backers seem to confirm that they think Tillis will be the GOP nominee. During the NCAA tournament — a veritable holy week in basketball-crazy North Carolina — Senate Majority PAC, a Democratic outside group, paid for television advertising linking Tillis to the Koch brothers. Hagan has focused her attacks on Tillis almost exclusively.

Tillis’s team views the attacks as evidence of his strength. “That’s part of what happens when you have a campaign that has momentum,” said Jordan Shaw, Tillis’s campaign manager. “That campaign’s going to get attacked.”

Hagan was elected in the Democratic wave of 2008, when she won just over 100,000 more votes than Obama did in North Carolina. But in a midterm election, when heavily Democratic younger voters and African Americans drop off significantly, Hagan’s team will struggle to turn out her base.

The Democratic Senatorial Campaign Committee, which is investing heavily in a turnout program it calls the Bannock Street Project, has identified 374,000 African Americans who voted in 2012 but not in the 2010 midterms, and 500,000 women who the party’s models say are likely to support the incumbent and who sat out 2010.

But Democrats also hope to appeal to independents who have been turned off by the state legislature’s conservative agenda over the past two years. Republicans in Raleigh, led by Tillis and Senate President Phil Berger (R), have pushed through major tax cuts, restrictions on abortion and changes to the state’s voting rules that infuriated Democratic groups; polls show the North Carolina legislature is only slightly more popular than Congress.

“This election is going to be a contrast between Kay’s bipartisan track record of common-sense results and her opponents who would rather push a fringe, special-interest agenda that was wrong for North Carolina when Thom Tillis passed it in Raleigh and is wrong for the state now that he’s pledging to take that agenda to Washington,” said Sadie Weiner, Hagan’s campaign spokeswoman.