This week, she met with Drs. Fauci, Stephen M. Hahn, the commissioner of the Food and Drug Administration, and Robert R. Redfield, the director of the Centers for Disease Control and Prevention, where the group talked through concerns about the Trump administration’s embrace of malaria drugs as possible treatments for Covid-19, the disease caused by the coronavirus, according to a senior administration official.

Publicly, Dr. Birx has been a soothing constant next to Mr. Trump and Vice President Mike Pence in coronavirus meetings and briefings, where she has been one of the few regulars in a rotating cast of health officials perched behind the White House lectern. Mr. Pence, who is overseeing the government’s response, introduced her at the time of her appointment as his “right arm.”

But on Thursday, that delicate balance appeared to tip. After talking to New York officials, Dr. Birx said she had been told that there were still intensive care beds and “over 1,000 or 2,000” ventilators still available. She also dismissed news stories of hospitals drafting blanket do-not-resuscitate orders for critically ill Covid-19 patients.

“To say that to the American people, to make the implication that when they need a hospital bed, it’s not going to be there, or when they need that ventilator, it’s not going to be there — we don’t have evidence of that right now,” she said.

Just a few feet away stood Dr. Fauci, a longtime friend and mentor of Dr. Birx’s, who had his own message: hunker down. He said that the coronavirus could become cyclical. He cautioned that a vaccine was still many months away. And he said that therapeutic treatments, which Mr. Trump has eagerly pushed as a “game changer,” were still unproven.

“The best way to get the best drug as quickly as possible is to do a randomized controlled trial so that you know is it safe and is it effective,” he said. “If it’s not effective, get it off the board and go to the next thing.”

The realities on the ground appear to favor the tone of Dr. Fauci’s warnings. Dr. Mahshid Abir, an emergency physician at the University of Michigan and an expert on hospital preparedness, said on Friday that shortages are inevitable. Hospital systems not only in New York but Atlanta, Seattle and New Orleans are already warning that they have or will reach capacity in the coming days.