Mr. Cuomo, speaking at the Javits Center in Manhattan, which the Army Corps is retrofitting into a 1,000-bed emergency hospital, said the rate of new coronavirus infections in New York is doubling about every three days. “We haven’t flattened the curve,” he said.

The peak of infection in New York could come in as little as two to three weeks, far earlier than previously anticipated, Mr. Cuomo said. The state now projects that it may need as many as 140,000 hospital beds to house virus patients, he said, up from the 110,000 projected a few days ago. As of now, only 53,000 are available.

As of Tuesday morning, New York State had 25,665 cases, with at least 157 deaths. There were around 15,000 cases in New York City alone.

Mr. Cuomo, once considered a bit player on the national stage, is emerging as the party’s most prominent voice in a time of crisis. His briefings — articulate, consistent and often tinged with empathy — have become must-see television. On Tuesday, his address was carried live on all four networks in New York and a raft of cable news stations, including CNN, MSNBC and even Fox News.

In a sign of the way Mr. Cuomo has become the face of the Democratic Party in this moment, his address even pre-empted an appearance by former Vice President Joseph R. Biden Jr. on ABC’s “The View” in New York. Mr. Biden called Mr. Cuomo’s briefings a “lesson in leadership,” and others have described them as communal therapy sessions.

The country’s second-biggest state is not on lockdown.

Gov. Greg Abbott on Tuesday continued to resist calls to issue a statewide order to keep millions of Texans in their homes as protection against the fast-moving virus, but he used strong language to encourage Texans to stay indoors. “The best thing that you can do to ensure that we are not spreading Covid-19 in the state of Texas is stay home, unless you need to be out,” Mr. Abbott said, referring to the disease caused by the coronavirus.

The country’s second-biggest state has been improvising its way through the crisis, influenced at times by the sheer span of Texas, by its partisan divides, by its rural-versus-urban split, by its top leaders’ support of Mr. Trump and by its small-government, low-regulation mythos.