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As Republicans look to pick up Democratic-held seats in their bid to gain control of the U.S. Senate, some are targeting an unlikely state -- Oregon.

The Beaver State has not elected a Republican in a statewide election since 2002. But some believe first-term incumbent Sen. Jeff Merkley is vulnerable, partly because of his enthusiastic support for ObamaCare in a state that had a disastrous rollout of its failed health care exchange, Cover Oregon.

The Republican primary will be held Tuesday, and it appears to be a two-person race between Dr. Monica Wehby and Jason Conger, two candidates with compelling personal stories who are quite different on social issues.

Wehby is a pediatric neurosurgeon with 30 years in the business of saving young lives. She was the first woman to graduate from UCLA’s neurosurgery program. But her claim to fame in this race, and a big reason why she’s getting support from influential Republicans nationally, is she was an early critic of ObamaCare. She was on the board of the American Medical Association and was featured in a 2009 ad opposing the Affordable Care Act.

“It’s a 2,700 page law, 20,000 pages of regulations now -- it’s impossible to work with this law,” Wehby said. “I think the best way is to repeal and replace with a plan that will actually work.”

Conger is a two-term representative in the Oregon State House. He’s also a practicing lawyer. While that might not seem so unusual, Conger’s path to the legal profession was anything but ordinary. His mother abandoned the family when he was young. So he lived with his father, often staying in trailer parks, and for stretches was homeless, sleeping in the back of his family truck.

From those humble beginnings in northern California, he graduated from Harvard Law School.

“I feel extraordinarily blessed to have been able to go from barely graduating from an alternative high school to graduating from Harvard Law School and living what I would consider the American dream,” Conger said.

Dr. Wehby has been endorsed by GOP heavyweights like Mitt Romney, Newt Gingrich and Dr. Ben Carson. She also received a major boost in the form of a $400,000 advertising campaign funded by the New Republican super PAC. Founded by Alex Castellanos, New Republican is attempting to pull the party more to the center. The group’s ads highlight Wehby’s credibility on ObamaCare, her sensitivity to issues important to women and her own professional background -- including a spot titled "Trust," which features the mother of a child whose life she saved with surgery many years ago.

Conger has raised far less money, and polls suggest he’s trailing. But he does have plenty of support, especially from social conservatives. Oregon Right to Life endorsed his candidacy and former presidential candidate Rick Santorum recently endorsed him in a radio ad. Conger also has wide support among Republican lawmakers in Oregon. He is strong on the Second Amendment, is staunchly pro-life and opposes gay marriage.

Wehby, who was raised Catholic, says she is personally pro-life, but would not work to take away abortion rights for other women. Wehby is divorced with four teenage children. She says she is not opposed to gay marriage. She believes the GOP can grow if it becomes a little more libertarian on social issues.

“We don’t want the government interfering in our business, in our personal lives, in our private lives, in our personal decisions,” Wehby said. “As Republicans, we want as little government interference in our lives as possible.”

The Republicans have been on a losing streak in Oregon ever since Merkley defeated Gordon Smith in 2002.

Mike Riley, of the Portland political consulting firm Riley Research, said gender politics do matter in the state.

“Republican men, particularly senior Republican men, have a very hard time attracting votes in Oregon," he said. "Among Democrats, of course, but independent women as well."

But Conger believes moving to the center is the wrong strategy.

“You don’t have to be moderate, you don’t have to abandon your principles,” he said. “You have to offer an alternative to voters to the incumbent, an alternative that is more attractive, that is credible and speaks to issues that they care about.”

Wehby might carry some baggage into the general election if she wins the primary. A number of recent stories raise questions about her relationship with a Republican donor who runs a large Oregon lumber company.

Andrew Miller, owner of Stimson Lumber, donated $31,000 to a super PAC that helped fund ads attacking Conger. It’s been widely reported that Miller and Wehby dated. The Oregon Democratic Party filed a complaint with the Federal Election Commission alleging there must have been coordination between Miller and the Wehby campaign, which would have made the donation a violation of campaign finance laws. Wehby told Fox News there was no coordination.

Politico is also reporting Miller accused Wehby of stalking him and harassing his employees as the couple was breaking up in 2013. No charges or restraining orders were ever filed.