COVID-19 patients could so overwhelm U.S. hospitals that doctors and nurses would be unable to provide adequately for other patients, an infectious disease specialist told CNBC on Wednesday.

"When you have emergency rooms flooded with patients, it makes it harder for us to attend to all the other issues," Dr. Celine Gounder said in a "Squawk Box" interview. "If you come in with a heart attack, we're going to be slower taking care of you and we're going to be sloppier with our own infection control if we're overwhelmed."

COVID-19 cases surpassed 1,000 in the United States late Tuesday. The coronavirus is now present in at least 35 states and the District of Columbia, according to the Centers for Disease Control and Prevention. Almost half of all U.S. cases are in Washington state, California and New York.

The U.S. has fewer doctors per person and fewer hospital beds per person than Italy, said Gounder, a clinical assistant professor of medicine and infectious diseases at New York University. Italy is among the hardest-hit countries outside China, where the virus originated in December. COVID-19 has infected more than 10,000 people in Italy, according to Johns Hopkins University, killing at least 631.

"We have less capacity to absorb a big surge in cases," she said. "We need to be preparing for that."

Gounder cares for patients at several hospitals, including Bellevue Hospital Center, where New York Mayor Bill de Blasio announced Tuesday that confirmed cases in the city had nearly doubled in one day to 36.

"They're coming in so intensely now that being able to give you a detailed case breakdown, we're not in that position to do that at this moment because there are so many coming forward," de Blasio said.

Dr. Mitchell Katz, CEO of NYC Health + Hospitals, said city hospitals are bracing for an onslaught of COVID-19 cases in part by preparing to discharge current patients. In the event of an emergency, they'll cancel outpatient surgeries and visits, he added.

"We are prepared at Bellevue and all of our hospitals, that were we to have many patients with respiratory distress, we would rapidly discharge those patients who are in the hospital now and do not need to be in the hospital because they can be safely cared for at home," Katz told reporters at Tuesday's news conference.