In contrast to 2018, Republicans otherwise will be almost entirely on defense in 2020 with Republican-held seats in Arizona, Colorado, Maine and North Carolina considered by both parties to be the top targets; seats in Iowa and elsewhere could move on to the list as the campaigns there develop.

Republicans believe they can hold on in most of the chief battleground states — Mr. Trump won two of the four in 2016, Arizona and North Carolina, and won one of Maine’s four electoral votes. And they say Democrats themselves are helping strengthen their hand.

Republicans in charge of the party’s overall Senate strategy say that the progressive agenda being embraced by leading Democratic presidential candidates and other prominent voices in the party — “Medicare for all,” the Green New Deal, public benefits for undocumented immigrants — is turning off the swing voters that Democrats will need to win Senate seats in places like Iowa and Arizona. Republicans are doing their best to brand Democrats as far out of the mainstream. The term “socialist” will be a regular feature of Republican ads and speeches.

“Every week Democrats offer up a different radical proposal that alienates mainstream voters in competitive states, so it’s best to let Democrats keep talking,” said Senator Todd Young of Indiana, the chairman of the National Republican Senatorial Committee.

Some Democrats privately agree but say the identity of the party’s eventual presidential nominee will play a more significant role in determining the outcome of the battle for the Senate. And while Republicans have sought to tie the progressive policies to top contenders such as Mark Kelly, the former astronaut and a prized Democratic recruit against Senator Martha McSally, Republican of Arizona, he and the other Democratic candidates have distanced themselves from proposals such as a government-run health insurance program that would end private coverage.

Democrats say that it is Republican candidates who are caught in a squeeze, trapped between independent and suburban Republicans uncomfortable with Mr. Trump and base voters who will brook no dissent when it comes to the president. Mr. Schumer noted that the same crosscurrents helped Democrats defeat the Republican senator Dean Heller in Nevada last year.