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

WASHINGTON — The battle for the White House may be the marquee political event of 2020, but it is the rapidly intensifying struggle for control of the Senate that will determine how power is truly wielded in Washington come 2021.

As Republicans assess President Trump’s uncertain re-election chances, they see maintaining control of the Senate as their last line of defense against the prospect of Democrats controlling both the House and the White House. Democrats view gaining the Senate as a way to stymie Mr. Trump should he win a second term. And they say that winning the White House only to have Senator Mitch McConnell, Republican of Kentucky and the majority leader, remain in charge of the Senate would stifle any legislative effort to undo the effects of the Trump presidency.

Strategists for both parties and independent analysts currently give Republicans the edge in narrowly holding on to the Senate given the small universe of highly competitive races. But the distinct possibility of wild cards adding to an already volatile atmosphere was underscored this week by the news that Senator Johnny Isakson, Republican of Georgia, will retire at the end of the year. His departure unexpectedly put another seat in play and gave Democrats a second pickup opportunity in a state they believe is trending increasingly blue.

“We have a decent shot,” said Senator Chuck Schumer, the Democratic leader. “Republican incumbents and Donald Trump are far weaker in the challenger states than people realize.”

Democrats would need a net gain of three seats to assume Senate control if they win the White House and four if they do not since the vice president serves as the tiebreaker in a 50-50 Senate. “The math is simple,” the advocacy group Emily’s List heralded in a fund-raising email, “the work is hard.”

Both sides agree that just a handful of seats are truly up for grabs at this point, limiting Democratic opportunities for the gains they want.

“They need to put another seat on the board or pull another rabbit out of their hat in Alabama and I’m not sure they can,” said Jennifer E. Duffy, who handicaps Senate races for the nonpartisan Cook Political Report.

Her Alabama reference points to the fact that Senator Doug Jones, a Democrat, faces re-election there after an upset victory in 2017 over Roy S. Moore, a former judge who was accused of sexual misconduct with teenage girls. Washington Republicans are determined to deny Mr. Moore a rematch. But other Republican candidates will be heavily favored in a very conservative state, making Mr. Jones the only seriously endangered Democratic incumbent at the moment. The party is defending a dozen seats compared with 23 for Republicans.

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.

“As Dean Heller learned, when they embrace Trump, they lose the middle, and when they run away from Trump, they lose the base,” he said in an interview, describing what he sees as the quandary for Republican incumbents in contested states.

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.

And both parties have their eyes on Kentucky, where Democrats would dearly love to defeat their nemesis, Mr. McConnell. But even if they cannot, they intend to focus on the race as a way of helping amplify the message that Democrats need to capture the Senate to thwart the man who has thwarted them so successfully. Mr. McConnell will be a part of every Senate race.

“Mitch McConnell is the Nancy Pelosi of 2020,” said Ms. Duffy, the analyst, referring to past Republican attempts to make the House Democratic leader the face of her party.