“The fact that we’re having this conversation, folks — this is real,” said Mr. Murphy, who enacted a statewide stay-at-home order just over two weeks ago.

New Jersey’s fatality and infection rates are still dwarfed by New York’s, where, as of Sunday, more than 122,000 people had been infected and more than 4,100 had died. The virus appeared to be spreading fastest in Nassau and Suffolk counties on Long Island, where there were more than 27,000 cases, only about 10,000 fewer than in all of New Jersey.

The outbreak in New Jersey is most serious in Bergen County, the state’s most populous county. It has recorded 6,187 confirmed virus cases and at least 189 deaths.

Teaneck, one of the county’s biggest townships, has reported 421 cases.

Ms. Acito said she expected her sister-in-law and brother-in-law, who were not on ventilators, to fully recover.

She said that she considered it a blessing to be able to visit with her relatives in person. “We know how fortunate we, as a family, are to have me on the inside,” she said in an interview on Thursday.

With hospitals closed to most visitors, nurses are the lifelines connecting patients and their families. At Holy Name, iPads wrapped in clear plastic to shield germs offer some patients the ability to communicate face-to-face with loved ones.

“Our role is not only to provide all this care, under these circumstances,” Ms. Acito said. “It’s to be their advocate, their family member, their provider.”