National Republicans see a chance to win the Oregon governor’s race as ballots hit the mail next week. Governor Tina Kotek faces a tough challenge from Republican Christine Drazan. John Horvick of DHM Research said, "If this were just a straight-up question, she would get destroyed," as polls show ties.

National Republicans, facing stiff headwinds in some of the most conservative parts of the country, see a ray of hope in an unlikely state: Oregon.

With Oregon's ballots set to hit the mail next week, Gov. Tina Kotek's quest for re-election in one of the country's most consistently liberal states is at risk of being derailed by a conservative, anti-abortion Republican, State Senator Christine Drazan.

Conservatives are not exactly surging statewide in the land of protest frogs and craft beer. But Ms. Kotek, a first-term Democratic governor, has managed to become almost as unpopular among her constituents as President Trump, whom they denounce routinely on the streets.

"If this were just a straight-up question, 'Do you want Tina Kotek to have another four years or not?' she would get destroyed," said John Horvick, senior vice president at DHM Research, a polling firm in Portland, Ore.

Oregonians haven't elected a Republican governor since 1982, and Ms. Kotek would seem well positioned to continue that streak. She went toe-to-toe with Mr. Trump last fall over his efforts to deploy National Guard troops to Portland amid immigration demonstrations and she has already defeated Ms. Drazan once.

Yet polls show this race between Ms. Kotek and Ms. Drazan essentially tied. A recent statewide poll conducted by Mr. Horvick's firm for Oregon Public Broadcasting found that 60 percent of potential voters viewed Ms. Kotek unfavorably, versus 63 percent for the president.

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