The hospitals that are marching on with the procedures feel they can safely do so, especially if they're not already seeing a surge in coronavirus cases. But some workers disagree, as they expect that more patients will flood the emergency rooms in the coming days. There's also a shortage of personal protective equipment at most health systems, which they feel needs to be conserved.

That's causing major disagreements among staff within hospitals. Several front line medical workers tell CNBC that surgeries they don't consider urgent have moved forward this week, which they believe threatens the health of employees and patients.

But there's a lot of variation in what hospitals consider elective and what they do not, including procedures that can reduce pain or discomfort but aren't life-threatening if they're delayed a few months. Some surgeons are continuing on with business as usual, even scheduling cosmetic procedures.

Many U.S. hospitals are canceling or scaling back on non-essential elective surgeries to make space for patients with the COVID-19 coronavirus and ensure there are enough intensive care beds available. Some states like Ohio are even moving to ban elective procedures altogether in the coming weeks. New York Mayor Bill de Blasio on Sunday said he would sign an executive order to suspend all elective surgeries at New York City hospitals.

Many hospitals and individual surgeons are grappling with tough questions about whether a procedure should qualify as urgent.

How about a patient undergoing a procedure that isn't immediately life-threatening to delay, but it could result in more serious complications in a few months?

"What if they don't get their frequently inflamed gallbladder removed, for instance, because it's deemed elective, then that could take a lot more resources overall to deal with if it becomes an emergency in a few months?" asks Dr. Dan Buckland, an emergency room physician at Duke Medicine.

But some medical workers believe hospitals are erring too far on the side of business as normal, and not taking the necessary steps to prepare for an influx of COVID-19 cases.

At UC Davis Medical Center, which treated some of the first coronavirus cases in the U.S., two medical providers said that supplies are being used to treat patients for procedures like routine colonoscopies or lipoma removals. These people believe the supplies should be conserved for COVID-19 patients. They said that throughout the course of the week, however, the list of procedures has been reduced, either because the surgeons have refused to take the case or the patient has proactively cancelled.

In addition, because of the lack of testing and shortages of protective gear, these people believe they might be exposed to the virus without realizing it. If they're infected without showing symptoms, they fear they might put other patients in harm's way.

The people declined to share their names for fear of repercussions from their employer.

In an emailed comment, a spokesperson for UC Davis Medical Center said on Wednesday that the hospital has not seen an uptick in COVID-19 cases, and it has a plan in place if that happens. "There is no need to implement a surge plan right now," they said, adding that the hospital has the "appropriate supplies" for various scenarios.

"We are continuing to offer scheduled surgeries for patients who are in need," the spokesperson said.

They noted that situation isn't black and white as many of the patients being treated at UC Davis Medical Center have a higher level of chronic illness and their cases are more complex. They might have no other options than to be seen at the hospital.

"About 25 percent of today's scheduled surgery cases are oncology-related, such as cancerous tumor removals, and another 25 percent of today's surgeries are injury-related, including injury repair, burns and post-injury care. The remaining cases are made up of procedures such as kidney stones, gallstones, and other surgeries for physical repair and patient pain relief," the spokesperson explained.

Nearby in Santa Clara County -- one of the first places in the U.S. to see coronavirus cases -- the CDC has asked hospitals to cancel all elective non-essential procedures. But three frontline health care workers at Stanford Medical Center described a process they say is allowing too many borderline cases to move forward.

These people, who declined to be named for fear of repercussions from their employer, said that surgical cases have been put into three buckets, depending on whether it's an emergent or elective case, or somewhere in the middle. Leadership weighs in if there's a disagreement.

But these workers say that some surgeons have been classifying elective procedures as non-elective and emergent in order to go ahead with them. One person offered examples of nerve decompression surgery, repairs of knee ligament tears, and wrist surgeries.

These people also say there's a lack of protective gear outside of cases where the patient is known or strongly suspected to have COVID-19. In going ahead with the elective procedures, they could be putting themselves — or patients — in harm's way. This seems sharply at odds with a recent order for all residents to "shelter in place" to avoid spreading the disease.

As one of the people put it: "If I can't go to a coffee shop in the Bay Area, should I be intubating someone regardless of whether they've been tested or are having symptoms?"

A Stanford Health Care spokesperson, in an email, said that special consideration will be given to patients with "certain underlying conditions that could increase risk if the procedure is delayed." But most elective procedures have been delayed. "The safety of our healthcare workers and patients is our top priority," they said.