The agency said it "expects" the drug to be delivered to every state and territory, but offered no timeline.

Luetkemeyer, for her part, says she understands the medicine needs to go to the hardest-hit communities. But the haphazard allocation of the drug, with no clear criteria for the regions getting it, is frustrating.

"My God, it's the first thing we've found that has a signal that it's working," she said. "And the safety signal is good too."

Luetkemeyer described a patient she cared for, knowing she couldn't give them remdesivir: "It's heartbreaking."

Doctors Don't Know Who Will Benefit Most

As physicians choose who gets remdesivir and who doesn't, doctors are to some extent flying blind. They want to give it to the patients who benefited most in the drug's large clinical trial, but the National Institutes of Health still hasn't published that study.

"We don't have a lot of data to work on," Walensky said, and "there's not a lot of history with this drug."

Lawmakers are also unhappy.

"A doctor making a life or death decision about how to allocate a limited amount of this drug and which patient gets it and which doesn't -- the clinical trials are very important in that regard. They haven't made that available," said Rep. Lloyd Doggett, the Texas Democrat who chairs the House Ways and Means Health Subcommittee.

In a statement, the National Institute of Allergy and Infectious Diseases told CNN that "the study team is currently reviewing the available data for the [clinical] trial and plans to publish a preliminary report of the initial results in the next few weeks."

Walensky said some doctors in her hospital have also turned down offers of remdesivir for their patients. Those patients appear to be on the mend, she said, and the doctors don't want to give them a new drug with limited benefits and so little history.

In a Washington Post op-ed last week, Walensky and others from Mass General said remdesivir has left doctors with more questions than answers.

"In the wake of this media bombshell and data tease," they wrote, "we are left with a treatment that the FDA has permitted us to use, and that patients and families will justifiably expect, but with an extremely limited drug supply and no evidence-driven guidance on how to use it."

Walensky said using a committee to choose which patients get the drug "is not how we like to practice medicine." But with so many patients -- and so little remdesivir -- the hospital decided it was the most equitable approach.

Equitable, though, doesn't mean easy, especially when it's unclear who needs the drug most. "It's a nearly impossible situation when your overarching mission is to do right," Walensky said.