When the top two Democrats in Congress sat down with President Trump in the Oval Office last week a day before the government was to shut down, they warned him that the coming fight was going to be politically painful for him and his party.
If Republicans failed to agree to extend expiring Obamacare subsidies, as Democrats were demanding as a condition of any government funding deal, Mr. Trump and the G.O.P. would bear the brunt of the blowback from voters, Senator Chuck Schumer and Representative Hakeem Jeffries, the two minority leaders from New York, told the president.
Prices would spike for around 20 million Americans, they added, including for many Trump voters.
Mr. Trump did not dispute the point, saying that Mr. Schumer and Mr. Jeffries were probably right, according to three people briefed on the private conversation who spoke on the condition of anonymity to describe it. But he quickly added that he and Republicans would deflect blame back onto Democrats.
The exchange helps explain why Democrats believe they have the political upper hand in the shutdown fight, and why they are refusing to back down from their demands, at least for now. They believe that Mr. Trump, who has long been sensitive to the political perils of health care issues for Republicans, could be the key to winning a commitment on the expiring subsidies that could end the crisis.
The White House did not immediately respond to a request for comment about the exchange.
Democrats are keenly aware that Republicans in Congress are divided on extending the subsidies, with some of them, including those from competitive states and districts, sounding the alarm about the coming premium increases.
“I made the point that the damage that’s being done to the health care of everyday Americans is hurting people who voted for him, and that is the reality,” Mr. Jeffries recently told reporters as he described the case he had made to Mr. Trump in the Oval Office that day. “It’s hurting everybody, but it’s certainly hurting people who voted for him.”