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In 2020, Republicans also face a hard time finding top-tier candidates for the Senate. The party so far hasn’t lured Gov. Chris Sununu of New Hampshire to run against Senator Jeanne Shaheen; President Trump has talked up his former campaign manager, Corey Lewandowski, but he is not precisely Everett Dirksen. Even in open Republican seats, the interest is minimal. Secretary of State Mike Pompeo has so far remained unconvinced that the seat in Kansas of Pat Roberts, who is retiring, would be a better gig than his current one. That has left Republicans contending with the conservative gadfly turned perpetual candidate Kris Kobach, who last year did the impossible, losing the Kansas governorship to a Democrat.

For Democrats, this is a high-stakes exercise. To retake control of the Senate, Democrats will need to pick up either three or four seats in 2020, depending on which party wins the White House. There are currently 34 Senate seats up for grabs, 22 of them held by Republicans. In every imaginable scenario — President Trump wins or loses, Democrats hold the House or lose it — taking back the Senate would be a boon for the party and its policy agenda, even if that is simply stopping Senator Mitch McConnell of Kentucky, the majority leader, from continuing to reshape the entire American judiciary.

“The two most important things about running for the Senate and winning, far more important than any others, are the Supreme Court and closing Mitch McConnell’s legislative graveyard,” said Senator Chuck Schumer of New York, the minority leader.

Democrats are quick to point out that the party has attracted strong contenders already for a few races.

The Speaker of the House in Maine, Sara Gideon, will take on Senator Susan Collins, the Republican from that state. Mark Kelly, the former astronaut and gun control advocate, is running against Senator Martha McSally in Arizona, who was appointed last year to fill Senator John McCain’s seat; Ms. McSally has already lost once to Senator Kyrsten Sinema, the Democratic freshman. Setting up a bit of farm-kid-on-farm-kid electoral violence, there is also Theresa Greenfield, a businesswoman, who is taking on Senator Joni Ernst, Republican of Iowa.

For some Democrats, the fact that Ben Ray Luján gave up a top House leadership post to run for a Senate seat in New Mexico (albeit a relatively safe one) is further evidence that the Senate is still considered awesome. And, again, Mr. Hickenlooper is considering it.