Mr. Walden grew up on a cherry orchard, worked at radio stations owned by his family, and followed his father into the State Legislature. The political shifts that have turned all three Pacific Coast states reliably Democratic have begun to creep into a few of the conservative inland parts of Oregon. Hood River County, long known for fruit farming, windsurfing and the spectacular scenery of the Columbia River Gorge, has lately become a center for the production of surveillance drones, leading to an influx of software engineers, technology entrepreneurs and other young professionals.

Mr. Walden’s margin of victory in November in the county where he lives was just five votes — out of more than 10,590 cast.

“It’s just a little left-leaning,” Mr. Walden allowed. “It didn’t used to be that way.”

Unlike many Republicans in Congress, Mr. Walden has worked productively with Democrats. “I’m a problem solver,” he said in an interview after a town hall-style meeting here near the Idaho border. “I’m not an ideologue. I want to fix things.”

And in Oregon, some Democrats and health-law supporters are glad Mr. Walden is in his position.

“I’ve known Greg a long time,” said Andrew S. Davidson, the president and chief executive of the Oregon Association of Hospitals and Health Systems. “He is not interested in upending the progress we have made in this state.”

Representative Kurt Schrader, a Democrat whose district includes the southern suburbs of Portland and the capital, Salem, predicted Mr. Walden “will be mindful of the implications of any legislation for our state, which is leading the nation in the transformation of health care.”

Unlike Mr. Walden, Oregon has embraced the Affordable Care Act. State officials say many of the changes proposed by congressional Republicans, including a rollback of federal funds for the expansion of Medicaid, would reverse much of the progress they have made.