Doctors and nurses on the front lines of the fight against the coronavirus in the United States say it's "the first time" they've been scared to go to work. With a shortage of personal protective equipment, some have resorted to using bandanas to cover their faces.

"It's the first time we've ever been truly scared to come to work, but despite being scared we are trained to save lives and we're committed to doing that," Dr. Cornelia Griggs, a surgeon in New York City, told "CBS This Morning." "I'm embarrassed to say, but prior to this, my husband and I had never gotten around to writing a will, but this weekend that became one of our to-do list items."

The government is sending medical supplies like masks, gloves and surgical gowns from the national stockpile to hospitals in need, U.S. Surgeon General Dr. Jerome Adams said, but some politicians and medical professions say that's not enough.

They have called on President Donald Trump to order private companies to produce the supplies under the Defense Production Act. Mr. Trump signed the act into law, but has not used it to order the production of the supplies.

"There are people that literally are wearing bandanas because they have nothing better than that to protect themselves from the respiratory droplets of patients who are infected with COVID-19, and I think that's a national shame," said Zaheer Shah, a primary care physician in Arizona.

Griggs said it "feels unimaginable" the medical professionals in the U.S. would be asked to use bandanas.

"I can tell you we're not at that point yet in New York City, but I will be outraged if it gets to that point," she said.

It's not just their own lives that health care workers worry about. "I'm scared for my loved ones. Honestly, I'm being as candid as I can be. I'm no hero, but I'm not scared about myself," Shah said. "I'm willing to bargain my own safety, but am I willing to bargain the safety of my child and my mother-in-law? I think that may be a bridge too far."

In addition to protective equipment, doctors are concerned about a shortage of ventilators. Without them, medical professionals will have to make "terrible triage decisions about who lives and who dies," said CBS News medical contributor Dr. Tara Narula.

"If you've never seen somebody gasping for air, it is a terrible thing to witness, and knowing that all you can do is stand there and watch them because you don't have a ventilator to intubate them, that's heart-wrenching," she said on "CBS This Morning" Monday.

Health care workers "need everybody to step in," Narula said. "We need every single American who's listening to this and listening to the plea of the health care workers to figure out what they can do to help in addition to the governments and the hospitals."