Both Parties See Control of the Senate as Pivotal. Here Are the Key Races They’re Watching.

Democrats say they see opportunity in the low poll numbers for embattled incumbents such as Senator Thom Tillis in North Carolina and Senator Susan Collins in Maine, who is facing the challenge of her political life after supporting the nomination of the Supreme Court justice Brett M. Kavanaugh as well as a tax bill that has proved unpopular with some in Maine. But Ms. Collins has shown in the past that she can overcome waves of discontent in her party and survive in a tough environment, similar to the way Senator Joe Manchin III, Democrat of West Virginia, has managed to defy the political odds in his state.

Democrats have struggled to land their preferred candidates in Georgia and Montana. They hold out hope that Gov. Steve Bullock of Montana will tire of his second-tier status in the contest for the Democratic presidential nomination and decide to run against Senator Steve Daines. John Hickenlooper, the former governor of Colorado, cheered national Democrats when he made that same switch to oppose Senator Cory Gardner, perhaps the most threatened Republican incumbent, in a state Mr. Trump failed to carry in 2016.

But Mr. Hickenlooper’s decision to run for the Senate after his presidential bid faltered — and the national party’s embrace of that move — have angered the 11 Democrats who were already running for Mr. Gardner’s seat and do not seem inclined to give him a pass.

National Democrats have rallied behind several other candidates facing primaries, including the speaker of the Maine House, Sara Gideon, who is challenging Ms. Collins, and Theresa Greenfield of Iowa, who will be stressing her deep farm roots against Senator Joni Ernst, who won a first term in 2014 by emphasizing her own farm background.

They also like their candidates with military credentials such as Mr. Kelly and Cal Cunningham, a North Carolina Democrat and veteran of Iraq and Afghanistan trying to unseat Mr. Tillis, who will face a primary of his own given Republican discontent with his performance.

Democrats believe they can potentially bring other races into play including Texas, where Senator John Cornyn, a former member of his party’s leadership, is running for a fourth term, and perhaps Kansas if Kris Kobach, a divisive Republican who lost the governor’s race last year, is the nominee for an open seat. Republicans have their eyes on Michigan, where John James, who lost a Senate race last year, is trying again with strong party backing against Senator Gary Peters, who Republicans think is vulnerable.