Jacky Rosen Wants to Flip Nevada for Democrats. But First, Kavanaugh.

“I’m not a politician,” she said, before reconsidering. “I’m not a career politician.”

But she knows a few. In early 2016, then-Senate Minority Leader Harry Reid — whose influence over the state’s Democratic Party has its own moniker, the “Reid machine” — handpicked Ms. Rosen to run for an open House seat. She won, even as Mr. Trump won her district. It was Mr. Reid, too, who helped persuade Ms. Rosen to run for Senate. Mr. Reid, through an intermediary, declined to comment.

“I tell my daughter who just graduated college, I always tell her, ‘Don’t not do something just ’cause it’s hard. Time is going to go by anyway,’” Ms. Rosen said.

Nevada’s electorate is divided between heavily Republican rural areas in the north and a growing Democratic population center around Las Vegas in the South. A growing number of Californians — left-leaning, Democrats hope — along with companies like Tesla and Google, are moving to the state, and the unemployment rate is below 5 percent. Its population is increasingly diverse. Because it is so split politically, Nevada’s statewide officials tend toward relative moderation.

Democrats believe Mr. Heller has weaknesses, including a political fiasco over health care that at turns infuriated voters of both parties. And in a state where Mr. Trump’s approval rating is upside down, Democrats believe Mr. Heller’s recent decision to align himself with the president is a liability.

Ms. Rosen’s supporters view her as a viable alternative, a left-of-center Democrat whose biography and sparse voting record leave Republicans with little to attack. She supports a Medicaid buy-in program. She wants comprehensive immigration reform and has backed stricter gun control legislation. If Ms. Rosen is understated — more Mojave Desert beige than Las Vegas neon — that, her backers say, is the point.

Mr. Heller, though, has never lost a race, and his defenders believe he will ultimately prevail.

“I think you have to have a very compelling reason to get rid of an incumbent U.S. Senator,” said Sig Rogich, a longtime Republican strategist in Nevada, “and there isn’t one.”