Mr. Trump, asked Thursday whether he agreed with Mr. McConnell that pandemic relief was “in sight” and whether he would support “this bill,” answered affirmatively. While it was initially unclear which bill Mr. Trump was willing to sign, the White House later clarified that it was the smaller Republican bill, which Mr. McConnell is backing.

“I will, and I think we are getting very close,” Mr. Trump told reporters.

Mr. McConnell’s plan is a nonstarter for Democrats, given that it would not provide funding for state and local governments or a revival of lapsed federal unemployment payments and would include a sweeping liability shield they have long resisted.

Democrats, who initially unveiled a $3.4 trillion proposal in May but later scaled back their proposal by about $1 trillion, argued that Mr. McConnell must drop his demand for a narrow package and consider the compromise plan centrists in both parties have proposed.

The bipartisan framework would restore lapsed federal jobless benefits, providing $300 a week for 18 weeks; would include $288 billion for struggling small businesses, restaurants and theaters and $160 billion for fiscally strapped cities and states; and would create a temporary liability shield for businesses operating amid the pandemic.

— Emily Cochrane The New York Times