Rachel Maddow and Chris Hayes at MSNBC, and Don Lemon at CNN, have all called for their own networks to stop televising the daily press conferences citing the amount of misinformation and propaganda that is broadcast.
A petition set up on moveon.org, that refers to the briefings as campaign rallies thinly disguised as news briefings, says that networks can continue to share the valuable, accurate parts, but there is no need for live coverage.
The petition has attracted 100,000 signatures in just three days.
Last week, Ms Maddow said that if it were to her: “I would stop putting those briefings on live TV. Not out of spite, but because it’s misinformation.”
On Monday night’s broadcast of All In, Mr Hayes bemoaned the fact that the briefings were supposed to be about imparting facts to the American people, but instead Trump is using them as “propaganda sessions” that are “dangerous from a public health perspective” and filled with misinformation and attacks on journalists and political enemies.
On CNN, Mr Lemon, host of CNN Tonight, debated with his colleague Chris Cuomo about the merits of showing the press briefings live.
Arguing that the network should only show relevant highlights, Mr Lemon said: “It’s obvious, it’s transparent to me. Those press briefings have become his new Apprentice. They’ve become his new rallies.”
Mr Cuomo disagreed saying that the public deserves to see “it all in real time”.
“I want people to see it all, we’ll question it all, we’ll show it all, and then they will decide how they’ve come through it,” he said.
One of the first calls to stop televising the press conferences came from the Washington Post 10 days ago, when Media columnist Margaret Sullivan wrote that the sessions were “ostensibly meant to give the public critical and truthful information about this frightening crisis — are in fact working against that end.”
“Rather, they have become a daily stage for Trump to play his greatest hits to captive audience members.”
Ms Sullivan cited Trump’s self-aggrandisement, media-bashing, and exaggeration and outright lies, as her principal reasons.
Sunday’s briefing saw Trump thank Jenn Pelligrino of One America News for her “nice question” about his standing in the polls, before then accusing PBS NewsHour’s Yamiche Alcindor of being “threatening” when she asked a question about ventilators.
At Monday’s briefing, introducing one of his staunch supporters, Trump said: “A friend of mine, Mike Lindell of MyPillow, boy, do you sell those pillows.”
Mr Lindell, whose factories are being retooled to make face masks, went off-script and literally praised the president, talking about how God had helped the nation change course with his election and that people should be using their time at home to read the Bible.
On MSNBC, Mr Hayes said about the network airing the briefing live: “It’s obviously above my pay grade, I don’t make the call that we take them or not, but it seems crazy to me that everyone’s still taking them when you got the MyPillow guy getting up there, talking about reading the Bible.”
On Tuesday morning the number of confirmed cases in the US was 164,516 and the number of deaths stood at 3,173 — more than the number that perished on 9/11.