Before its request for emergency funds, the Trump administration had said it could shuffle money between accounts to fund its coronavirus response, pulling from a $105 million Centers for Disease Control and Prevention rapid response fund and upward of $136 million diverted from other federal programs.

Senator Bill Cassidy, Republican of Louisiana and a physician who regularly works on health issues in Congress, said that when he met this month with Dr. Robert R. Redfield, the C.D.C. director, he was told that the funding it had then was sufficient.

“There was no, ‘We need help,’” Mr. Cassidy said.

Lawmakers have been skeptical. The president’s budget request for the fiscal year that begins in October would slash the C.D.C.’s budget by almost 16 percent, and the Health and Human Services Department’s by almost 10 percent. Tens of millions of dollars would come from the department’s Office of Public Health Preparedness and Response and its Hospital Preparedness Program, which helps hospitals handle surges of patients during disease outbreaks.

The administration also proposed cutting more than $85 million from the C.D.C.’s National Center for Emerging and Zoonotic Infectious Diseases. The center directly works on outbreaks like the coronavirus, which is believed to have emerged from live animals in Wuhan, China.

Before the coronavirus outbreak, the Trump administration had already narrowed its epidemic work in countries around the world. Its latest budget request included $3 billion in cuts to global health programs, including a 53 percent cut to the World Health Organization and a 75 percent cut to the Pan American Health Organization.

At a Senate hearing this month, Alex M. Azar II, the secretary of health and human services, said that his budget prioritized the C.D.C.’s infectious disease program and his department’s hospital preparedness efforts, and that the C.D.C. had begun working with local health departments to test people with flulike symptoms for the coronavirus.