Monica Wehby, the Republican candidate for Senate in Oregon, is billed as an “independent conservative.” (Stephanie Yao Long/AP)

To Republicans, the Senate race in this solidly Democratic state presents an alluring opportunity. Oregon’s health insurance exchange has been one of the country’s most troubled. President Obama’s approval rating has fallen below 50 percent. Sen. Jeff Merkley, a liberal Democrat first elected on Obama’s coattails in 2008, is not terribly well known.

And in Monica Wehby, Republicans have a fresh-faced, female challenger who they believe matches the moment: a pediatric neurosurgeon and political outsider who rails against the Affordable Care Act but is relatively moderate on social issues.

Republicans don’t need Oregon in order to win back the Senate this year. But they do need to make inroads in blue states such as this one to compete for the White House in 2016. To expand its reach beyond older white men in the Deep South and the Midwest, the GOP must persuade voters to switch sides for candidates like Wehby.

“Unless we conservatives learn how to compete and start winning in swing and blue states, we will never govern America,” said Mike Murphy, a veteran Republican strategist.

Mathematically, Republicans can pick up the six seats they need to gain control of the Senate by winning only in states that GOP presidential nominee Mitt Romney carried in 2012. Still, they are trying to expand the playing field to include seven states Obama won: Colorado, Iowa, Michigan, Minnesota, New Hampshire, Oregon and Virginia.

Election Lab: See our current forecast for every congressional race in 2014

Republican officials are particularly optimistic about Iowa, where Rep. Bruce Braley, the presumptive Democratic nominee for an open Senate seat, could be vulnerable, and about Colorado and New Hampshire, where Republicans recruited top-tier challengers to take on first-term Democratic incumbents.

Here in Oregon, Wehby has drawn praise from national GOP luminaries and attracted notice with a moving television ad about how she saved a newborn with spinal problems. She also has a catchy slogan: “Keep your doctor, change your senator.”

But Wehby has gotten off to a rocky start in her general-election campaign. After police reports detailing domestic disturbances involving her ex-husband and an ex-boyfriend surfaced two weeks ago, she largely hid from the media and has struggled to regain her footing.

The GOP’s shadow

The bigger problem for Wehby, however, may be the GOP brand itself. She is campaigning as a different kind of Republican, with softer edges and a libertarian streak. But she has had difficulty distinguishing her candidacy from her party’s more strident national agenda.

“The Republican brand is in a sad state across the country, but particularly so in places like Oregon,” Democratic pollster Geoffrey Garin said. “There are a host of things that Republicans are routinely for that very frequently become deal-breakers for voters.” He cited restrictions on women’s access to abortion and contraception as examples.

For Democrats, the key to winning the Senate majority in 2006 and keeping it ever since has been ideological flexibility. Democrats like Heidi Heitkamp of North Dakota and Mark Begich of Alaska got elected by carefully tailoring their campaigns to their deep-red states and rejecting liberal orthodoxy on some issues.

Wehby is attempting to adopt a similar strategy. A political newcomer with no voting record, she has taken stances on hot-button social issues that are out of step with the GOP base but designed to appeal to moderate voters.

On abortion, she has said that she is personally pro-life but that it is a choice that should not involve the federal government. On same-sex marriage, she has said only that it is a “personal decision” and “not a government decision.” And on immigration, she has said that she opposes amnesty for illegal immigrants but that she wants to provide them a path to legal status.

“Voting completely with one party or the other is not representative of Oregon because we’re a purple state,” Wehby told the Oregonian. “I’m not going to go and rubber-stamp things.”

When pressed, however, she could not cite a specific policy disagreement with a majority of Senate Republicans.

A populist Democrat

That could spell trouble for Wehby. Merkley has begun running a populist campaign, casting her as another Republican in the mold of Romney, who was characterized by Democrats as an out-of-touch plutocrat.

In an interview with The Washington Post at his Portland campaign headquarters, Merkley listed pocketbook issues such as pay equity, raising the minimum wage and expanding unemployment insurance as areas where he and Wehby disagree.

“She has said she couldn’t think of one thing she differed from the national Republican agenda on,” Merkley said. “It’s not okay. [The] national Republican agenda is all about helping the best off get better off, and it’s the opposite of my fight for working families.”

He added: “I don’t suppose there are a lot of senators who live in a working-class community, but I do. . . . There are two foreclosed homes on my street.”

Merkley lives in a multi-ethnic neighborhood on the eastern edge of Portland. Wehby lives in a well-to-do Portland suburb and, according to a police report, drives a Mercedes.

The next day, Merkley brought Sen. Elizabeth Warren (D-Mass.) to Portland for a campaign fundraiser and rally, where she whipped up a crowd of 1,000 people with fiery attacks on big banks, chief executives, lobbyists and Republican lawmakers.

“The game is rigged, and it’s up to us to change it,” Warren said. With Merkley at her side, Warren called this fall’s campaign “a fight over values.”

At the rally, Jean Eilers, 73, a retired union organizer, said she worries that Wehby could come on strong against Merkley.

“She makes me nervous,” Eilers said. “She’s a woman and she’s a doctor, and she has a calmer tone. But once you see who’s supporting her, it will be clear to people in Oregon what she’s really about.”

Major GOP super PACs have not yet spent much money in Oregon, although a group called New Republican aired TV and radio ads on Wehby’s behalf during the primary, calling her an “independent conservative.”

Alex Castellanos, a leading GOP strategist who founded New Republican, characterized Wehby as the type of candidate Republicans need to champion.

“If we remain what we are now — the party of ‘No,’ the party more interested in telling you what you can’t do and what you can’t be — and we can’t win in a place like Oregon, we’ll be a party that’s left behind,” he said. “Unless we expand our playing field and offer an optimistic vision of how we take people to a better place, there isn’t enough map for us.”

Wehby declined The Post’s request for an interview. She also has refused to speak with most in-state media since May 16, when news broke of a 2013 police report in which her ex-boyfriend, Andrew Miller, accused her of stalking him. The police report, which the Oregonian said was first obtained by a state Democratic Party researcher before Politico reported on it, roiled Wehby’s campaign leading up to the May 20 primary.

In two separate episodes that were later reported by the Oregonian, Wehby’s now ex-husband, Jim Grant, also called police in 2007 and 2009 complaining that she had been harassing him.

Wehby’s Washington-based consultants and operatives with the National Republican Senatorial Committee (NRSC) have been helping her manage the scandals. Last week, Wehby held a few small public events, but they were in rural parts of the state and her campaign did not announce them until an hour beforehand, making it logistically impossible for Portland-based reporters to cover her appearances.

“It’s a sign of a rookie candidate,” said Jim Moore, a political scientist at Pacific University. “Now it’s basically up to her to learn how to respond to those stories and to move on and put together a strong candidacy.”

Merkley, in his interview with The Post, refused to comment on Wehby’s personal life but criticized her for dodging the media.

“I do strongly believe that if you are running for office, citizens have a right to absolutely hear your response to the issues that are before us,” Merkley said, noting that Wehby had declined to debate her GOP primary opponents.

An ‘unwinnable’ state?

Democratic officials contend that Oregon has become “unwinnable” for Republicans. Although for much of the last century it was represented by two Republican senators, Oregon has not elected a Republican statewide since then-Sen. Gordon Smith in 2002.

But GOP officials believe that Merkley is vulnerable this year. They say the problems in implementing Cover Oregon, the state’s health insurance exchange, could weigh him down. And they argue that Merkley’s recent achievements — pushing filibuster reform, preventing Lawrence H. Summers from being nominated to chair the Federal Reserve Board and opposing military action in Syria — are not motivating issues for most voters.

With the right independent-minded candidate, GOP operatives think they can reverse the trend in Oregon.

“The path to victory starts with a vulnerable incumbent, and that’s exactly what Sen. Jeff Merkley is,” said Kevin McLaughlin, an NRSC consultant who has advised Wehby. “Then, Republicans have to nominate someone who gives you a chance to capitalize on that vulnerable incumbent — like a moderate woman who is a Washington outsider who also happens to be a pediatric neurosurgeon.”