Faced with the grim prospect that 200,000 Americans could die even with aggressive action to slow the spread of the coronavirus, President Trump extended the guidelines on avoiding nonessential travel, staying away from work, visiting bars and restaurants and gathering in groups of more than 10 for at least another month. “We can expect that by June 1, we will be well on our way to recovery,” Mr. Trump said on Sunday evening. “We think by June 1. A lot of great things will be happening.” But the virus has already dashed Mr. Trump’s earlier rosy predictions, and as Americans entered their third week living in a work-from-home world, officials warned that the deepening crisis in New York was weeks from peaking. “Thousands of people will pass away,” Gov. Andrew M. Cuomo warned. “I wouldn’t be surprised if we saw over 100,000 deaths,” Dr. Anthony Fauci, the United States’ leading infectious disease expert, said on Monday.