WASHINGTON — In his two newest campaign advertisements, Gov. Steve Bullock of Montana portrays himself as a health care savior, featuring local nurses who say his expansion of public health insurance rescued Montanans and their hospitals.

Steve Daines, the first-term Republican senator whom Mr. Bullock is trying to unseat, has his own ad, accusing the governor, a Democrat, of favoring “government-controlled” health care.

The dueling commercials illustrate a reality of the accelerating campaign season, which is entering a crucial period as the coronavirus pandemic continues to rage: Health care is shaping up as a driving force in deciding the outcome in November.

Its salience has been amplified by the pandemic and accompanying job losses that have left millions of Americans anxious about their own health and ability to pay medical bills. And the contrast between Republicans and Democrats could not be starker than it has been in recent weeks, as the Trump administration pushed forward with its lawsuit calling on the Supreme Court to jettison the Affordable Care Act once and for all, and House Democrats countered by passing a bill to expand it.

The fight over health care is being waged at the presidential level, in all of the competitive Senate races and in House contests across the country. Democrats intend to press what they see as their advantage over Republicans, who for years have called for dismantling the health care law — voting to repeal it and supporting President Trump’s legal efforts to overturn it — while failing to offer an alternative plan.

Democrats are eager to replay their winning strategy of 2018, when they won control of the House by emphasizing that Republicans were threatening to strip away protections for pre-existing health conditions and leave sick Americans on their own.

“It’s 2018 again, but on steroids,” said Leslie Dach, the chairman of the liberal advocacy group Protect Our Care, which has been fighting Republican efforts to overturn the Affordable Care Act. “Trump has put the Republican Party totally on the wrong side of this.”

The battle is also likely to figure prominently in the coming negotiations over the next coronavirus recovery package in Congress, which Republicans are planning to use as a vehicle to try to redeem themselves with voters on health care by offering provisions aimed at meeting medical needs stemming from the pandemic. Top Republicans say they see their legislative response to the virus as paramount to voters.

“I think the virus spending is more important than the other health care issues,” said Senator Roy Blunt, the Missouri Republican who chairs the Appropriations subcommittee on health spending and is involved in Republican efforts to assemble the plan to be unveiled this month.

Democrats and their allies say they do not believe that any action before November by Senate Republicans will be enough to neutralize the issue, given the party’s extensive history of trying to overturn the health care law without putting forth any alternative. They point to recent polls that show Democrats are far more trusted on health care than congressional Republicans or Mr. Trump.

And they are pressing their case in campaigns across the country through an array of ads aimed at Republicans. Last week, Protect Our Care began a $2 million advertising campaign in Arizona, Michigan and Wisconsin — all key battlegrounds — condemning Mr. Trump’s response to the pandemic. One highlighted the toll the virus had taken on those in nursing homes and other older Americans.

“This crisis did not have to be as bad as it was,” a health care worker says at the end of one such spot.

On Thursday, Majority Forward, a group aligned with Democrats, began part of a $3 million ad campaign in Georgia accusing Senator David Perdue, the Republican incumbent, of siding with insurance companies over beneficiaries, “even during a pandemic.” The group began a similar seven-figure effort in Colorado against Senator Cory Gardner, the endangered Republican incumbent.

In one of his first ads after securing the Democratic Senate nomination to oppose Mr. Gardner, John Hickenlooper, the former Colorado governor, called it “lunacy” that the Trump administration would press a lawsuit to overturn the Affordable Care Act during a pandemic. These efforts follow earlier health care attacks on Senators Martha McSally of Arizona, Thom Tillis of North Carolina and Joni Ernst of Iowa, all incumbent Republicans.

Democrats say voter anxiety about health care has been exacerbated by the Trump administration’s decision to again ask the Supreme Court to take the health care law off the books. The administration filed an extensive brief making its case in late June, joining Republican officials from 18 states in calling for action that could eliminate coverage for as many as 23 million Americans. Democrats are eager to pounce.

“Health care is a major issue for voters and a liability for every Senate Republican on the ballot,” said Lauren Passalacqua, a spokeswoman for the Democratic Senatorial Campaign Committee. She noted that Republican leaders were “in court right now trying to tear down health care access in the middle of a pandemic. It’s reckless and out of touch, and we’ll make sure voters have the facts in November.”

Even some Republicans say the lawsuit is seriously misguided.

“It was never a good move — never,” said Senator Susan Collins of Maine, who is facing a steep re-election challenge and was one of three Republicans to oppose the repeal of the health care law in 2017. “But to do it in the midst of a pandemic defies logic.”

Other Republicans are leery of the lawsuit’s timing but reluctant to oppose it given the longstanding opposition to the health care law among conservative voters, for whom calls for repeal of the Affordable Care Act have become dogma. Endangered Republicans are bracing for the attacks.

“I’m sure they’re going to try to make the most of it,” said Senator John Cornyn, a Texas Republican on the ballot this year.

He and other Republicans say their support for repealing the health care law does not equate to ending coverage for pre-existing conditions — a top concern of voters worried about their coverage.

“First and foremost, regardless of what is going on, we need to ensure that those with pre-existing conditions are being taken care of,” Ms. Ernst said.

The issue has surfaced in dozens of House races as well. In Central Illinois, where Betsy Dirksen Londrigan, a Democrat, fell one percentage point short of defeating Representative Rodney Davis in 2018, she is hammering a health care-centric message against him in the rematch contest. She held a news conference two days after the House vote to expand the health care law in which she condemned Mr. Davis’s vote against the bill, saying that he and other Republicans had waged “an all-out assault on the Affordable Care Act and on people with pre-existing conditions.”

Mr. Davis issued a statement calling the Democratic measure “partisan legislation that does nothing to lower the overall cost of health care.” His campaign assailed Ms. Londrigan’s support for “Medicare X” legislation that would allow people to buy in to a new public health insurance plan that used Medicare’s network of providers and would be similarly priced, saying it would devastate health care providers.

Yet Republicans concede they have not put forward a comprehensive alternative to the health care law despite Mr. Trump’s promise to deliver better and cheaper coverage. They are now pledging to put significant health care aid in the pandemic response legislation that Congress hopes to deliver by the beginning of August.

“I think on the health care part, there’s realization we’re going to have to do more, because unfortunately, in some of our states, we’ve seen the numbers start to go back up again,” Senator Rob Portman, Republican of Ohio, said this month.

Democrats and their allies say that any health care push by Republicans is likely to be too little too late to blunt the political consequences of their records.

“In 2018, health care helped cost them the House,” said Jesse Ferguson, a Democratic strategist who specializes in health care policy. “Since then, they’ve added a dash of lawsuit and poured it over a bed of coronavirus — all of which made it even worse for them.”

In Montana, Mr. Daines decided to take the offensive with his ad, in a which a doctor in the state says the senator supports coverage for pre-existing conditions, while Mr. Bullock is aligned with Speaker Nancy Pelosi and former Vice President Joseph R. Biden Jr., whose “liberal” plan would put “government bureaucrats between me and my patients.”

“Democrats showed the entire county what their objectives are on health care during the presidential primary: a government-controlled plan that seeks to employ employer-based coverage,” said Jesse Hunt, a spokesman for the National Republican Senatorial Committee.

During his brief presidential run, Mr. Bullock broke with progressive Democratic rivals in opposing the Medicare for All plan in favor of adding a public option to the Affordable Care Act. In his own ad, the governor wins praise for bringing Republican and Democratic legislators together to agree to expand federal Medicaid coverage that his campaign says has been a lifeline to rural hospitals.

Seeing the issue as a winner, Democrats say they welcome attempts by Mr. Daines and other Republicans to push the health care debate to the forefront.

“I think Democrats in general are totally fine with having that fight with our Republican opponents,” said Olivia Bercow, a spokeswoman for Mr. Bullock.