North Carolina Sen. Kay Hagan was supposed to be one of the most vulnerable Senate Democrats this year but she has managed to consistently lead in the polls, as Republican challenger Thom Tillis struggles to muster the support of tea party voters he needs to win in November.

Mrs. Hagan meanwhile is energizing her base by accusing Mr. Tillis, speaker of North Carolina’s House, of being a right-wing extremist who she characterizes as anti-woman and anti-education.

“While Kay was named the most moderate member of the Senate Speaker Tillis led a deeply unpopular legislature that cut education spending by $500 million to give tax breaks to the wealthy, killed an equal pay bill, refused to raise the minimum wage and defunded Planned Parenthood,” said Hagan campaign spokesman Chris Hayden.

From his career in corporate America to his support of toll roads to his comment that legal gay marriage is likely inevitable, Mr. Tillis has alienated much of the state’s conservative base, said Thomas Mills, a Democratic political analyst in North Carolina.

“If you’re living in a town of 2,000 people in rural North Carolina that’s the base,” he said. “He culturally can’t connect with those people. He’s not a tea party guy and they never accepted that he is.”

Joe Greene, a leader of the Conservative Patriots Of Wilkes Empowering the Republic, or CPOWER, a tea party group in Wilkes County, agrees.

“He’s an establishment Republican. That’s why I’m opposed to him,” said Mr. Greene. “A lot of people feel the way I do and won’t vote for him. He’s got a lot of things about him that’s not grass roots.”

He said that unlike many of his tea party compatriots, he would begrudgingly cast his ballot for Mr. Tillis.

Asked if he thought Mr. Tillis would win, Mr. Greene said: “Right now, I kind of doubt it.”

Mrs. Hagan has edged out Mr. Tillis in nearly every major poll, albeit usually by a thin margin. She reached the important 50-percent threshold in a Civitas poll this week, topping Mr. Tillis 50 percent to 43 percent.

The Tillis campaign did not respond to questions about the candidates’ support from tea party and conservative voters.

Mr. Tillis‘ low poll numbers are a headache for the national Republican Party, which is eyeing North Carolina for a Senate seat pickup. Mrs. Hagan’s seat was considered one of the easier pickups in Republicans’ quest of a net gain of six seats this year to win majority control of the Senate.

David Rohde, a political science professor at Duke University in Chapel Hill, North Carolina, said that Mr. Tillis‘ role as speaker had put him a political bind similar to that of House Speaker John Boehner, Ohio Republican. Mr. Boehner also gets hit from the right for not being conservative enough and from the left for being extremist.

Fittingly, Mr. Boehner this week sent one of his top aides, Michael Steel, a North Carolina native and experienced campaign operative, to help out with GOP campaigns in the Tar Heel State.

The Duke professor said Mrs. Hagan caught a lucky break when Mr. Tillis won the Republican primary.

“I don’t know that I’d say Tillis was blowing it, but he’s the reason she’s doing well,” said Mr. Rohde.

Mr. Tillis has moved to shore up his conservative base. He brought in tea party favorite Sen. Rand Paul for a campaign event Wednesday.

Mr. Paul, a Kentucky Republican who is considering a 2016 presidential run, vouched for Mr. Tillis‘ conservative credentials.

“Lower taxes, the Constitution, limited government, balanced budget, personal liberties. I think Thom represents those ideas,” he told a crowd at Big Ed’s restaurant in Raleigh, the city’s News & Observer reported.

Mr. Tillis has won over some tea party voters, just not enough to boost him in the polls. The worry among Tillis‘ supporters is that he’ll have the same problem on Election Day.

“He’s accomplished more for the state of North Carolina than Jesse Helms did,” said Tom Kern, president of the Catawba Valley Tea Party in Hickory, a small city about 50 miles northwest of Charlotte.

Mr. Kern said that Mr. Tillis won him over when the two met in person at an event early in the campaign.

The two sat together on a picnic bench and Mr. Tillis went over this record of conservative accomplishments, including passing voter ID laws, protecting gun rights, restricting abortion and balancing the state budget.

Mr. Kern blamed Mr. Tillis‘ campaign advisers for sapping tea party support by pushing the candidate to the center in an attempt to peel off Democratic voters from Mrs. Hagan.

“It’s wrong. He’s got to energize the base,” said Mr. Kern.

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