Many hospitals are not only swamped with cases but severely shorthanded because of so many employees are out with Covid-19.
At the same time, Omicron appears to be causing milder illness than the Delta variant.
Last month, the Center for Disease Control and Prevention said that health care workers who have no symptoms can return to work after seven days with a negative test, but that the isolation time can be cut further if there are staffing shortages.
France last week announced it is allowing health care workers with mild or no symptoms to keep treating patients rather than isolate.
In the Phoenix area, Dignity Health, a major hospital operator, sent a memo to staff members saying those infected with the virus who feel well enough to work may request clearance from their managers to go back to caring for patients.
"We are doing everything we can to ensure our employees can safely return to work while protecting our patients and staff from the transmissibility of Covid-19," Dignity Health said in a statement.
In California, the Department of Public Health said the new policy was prompted by "critical staffing shortages". It asked hospitals to make every attempt to fill openings by bringing in employees from outside staffing agencies.
Also, infected workers will be required to wear extra-protective N95 masks and should be assigned to treat other Covid-19-positive patients, the department said.
The 100,000-member California Nurses Association came out against the decision and warned it will lead to more infections.
Governor Gavin Newsom and other state health leaders "are putting the needs of health care corporations before the safety of patients and workers", Cathy Kennedy, the association's president, said in a statement. "We want to care for our patients and see them get better — not potentially infect them."
Earlier this month in Rhode Island, a state psychiatric hospital and a rehabilitation centre allowed staff who tested positive for Covid-19 but were asymptomatic to work.