Eager to offer an alternate narrative to the one Mr. Trump has been presenting, the two are trying to play on what they regard as Mr. Trump’s biggest political weakness: For all the talking the president is doing, many Americans do not believe what he says.

Polls show that Mr. Trump’s rambling briefings, delivered from the White House briefing room or the Rose Garden just outside, are doing him little good. His job approval ratings, which saw a slight uptick when he first took to the airwaves, are stuck near 46 percent, the same as before the pandemic, according to an average calculated by Real Clear Politics. Surveys show that most Americans think the president waited too late to respond to the novel coronavirus. The nation’s governors are getting far better grades from the public.

Ms. Pelosi and Mr. Schumer, looking toward the November elections amid deep anxiety among Americans about the pandemic, are trying to weaponize those sentiments. Sidelined from the Capitol, they lack Mr. Trump’s powerful megaphone. Ms. Pelosi is conducting interviews in front of a laptop in her well-appointed kitchen, with her high-end appliances in the background. Mr. Schumer has set up his iPad on a pile of books atop his dining room table in Brooklyn.

“It’s supposed to be at eye level,” he explained in an interview Thursday.

Despite their considerably less grand backdrops, the two have managed to play jujitsu with the president, by either baiting Mr. Trump with their own television appearances or commandeering at least some portion of his briefings by raising questions, reiterated by reporters who then push him to respond.

“Even if the public doesn’t hear them directly, Schumer and Pelosi still play a very influential role in shaping the debate in a way that affects what Trump has to answer for when he does his media circus,” said Geoff Garin, a Democratic pollster. “They may not always have the ear of the public, but they have Trump’s ear, and he is hypersensitive to what they have to say.”