WASHINGTON >> As the toll of the coronavirus continues to rise — with more state shutdowns, extensive new layoffs and overwhelmed hospitals — lawmakers and administration officials are turning their focus to what more is needed to counter the pandemic and protect a battered economy.

President Donald Trump, in a stark change of tone, told Americans today that the peak of fatalities from COVID-19 will not arrive for two more weeks, pleading with the public to continue social distancing in order to get through “a very vital 30 days” that would be a time of national challenge.

“This is our shared patriotic duty,” he said at a news conference in the White House Rose Garden. “We’re sort of putting it all on the line, this 30 days — so important because we have to get back. But the more we dedicate ourselves today, the more quickly we will emerge on the other side of the crisis, and that’s the time we’re waiting for.”

Officials are beginning to outline elements of another government relief package to add to the federal response, only days after Trump signed into law a $2 trillion economic stimulus, the largest in American history.

“We have a list of issues that are immediate — that have a short fuse,” said Speaker Nancy Pelosi, in a nearly 40-minute telephone interview today from her office in the Capitol. She ticked off a list of Democratic priorities, including increased protections and equipment for workers on the front lines of the coronavirus, expanded paid leave, a major new infrastructure investment and additional funds for state and local governments.

“This isn’t about how fast we can do it,” she added. “It’s how fast we must do it.”

It is not clear how quickly such a bill could materialize — Republican leaders and Steven Mnuchin, the Treasury secretary, have said they are not yet certain that more help would be needed, or when — but in outlining her plans today, Pelosi made it clear that the path to any further government assistance would run through her office, and that Democrats would press for another large package sooner rather than later.

By this afternoon, more than half of the 50 states were under a directive to remain at home, meaning that roughly 3 out of 4 Americans are or will soon be asked to avoid leaving their homes as part of a broad effort to stall the spread of the virus.

Dr. Anthony S. Fauci, the United States’ leading infectious disease expert, said that the country as a whole would see the death toll rise. “I wouldn’t be surprised if we saw over 100,000 deaths,” he said.

The Comfort, a Navy hospital ship, docked in Manhattan today to provide relief to New York’s overwhelmed hospitals and help treat patients who do not have the coronavirus. And even with billions of dollars in funds being allocated to both states and hospitals, officials say more will probably be needed as the virus continues to spread and portions of the economy continue to shutter.

More than 66,500 cases had been identified in New York state by today, with the death toll surpassing 1,200, by far the most of any state.

Virginia and Maryland, as well as the District of Columbia, issued new orders today for residents to stay home. And in Florida, Gov. Ron DeSantis, a Republican who had resisted a statewide edict, said that he would sign a directive codifying a patchwork of local rules urging residents in the densely-populated southeast corner of the state — including Miami-Dade, Broward, Palm Beach and Monroe counties — to stay at home.

In Washington, Pelosi and other officials involved in previous negotiations have acknowledged that it is unlikely that any legislation to address the crisis would be ready for a floor vote before mid-April, with both the House and Senate in recess and not scheduled to return to Capitol Hill until April 20.

Some officials involved in the talks, including Rep. Kevin McCarthy of California, the minority leader, have suggested there may be no need for another round of government relief. Mnuchin, who had previously said he expected a second round of direct payments to Americans would be needed, also said Sunday that he hoped it would not be needed.

In less than four weeks, Congress has approved and Trump has signed into law three bills totaling more than $2 trillion worth of government aid, including a significant expansion of the social safety net and a $500 billion bailout for distressed companies — a stunning outpouring of federal resources that is only beginning to be put into effect across the country.

But even before the stimulus measure was complete, Pelosi had begun laying the groundwork for a far-reaching fourth measure, including at a ceremony right after the legislation passed the House.

In the interview today, Pelosi emphasized the need to secure more equipment for health workers on the front lines, known as personal protective equipment, and ventilators for hospitals. She said Democrats would most likely revisit a push to boost pensions and medical leave provisions, and would work to ensure that other aspects of treatment for the coronavirus, beyond the initial test, would be covered by the government.

She also said she would like to see more measures aimed at getting money directly into the hands of individuals and families, including a possible retroactive rollback of the limit on the state and local tax deduction, a change that hurt high earners in states like New York and California.

“They’d have more disposable income, which is the lifeblood of our economy, a consumer economy that we are,” Pelosi said.