NEW YORK — Stocks on Tuesday recouped most of their historic losses from the prior day as hopes rose, faded and then bloomed again on Wall Street that the U.S. government will try to cushion the economic pain from the coronavirus.

The day’s moves were a microcosm of the severe swings that have dominated recent weeks, and market watchers say they are likely to continue until the number of infections stops accelerating. In the meantime, investors want to see a big, coordinated response from governments and central banks to shore up the virus-weakened economy.

The S&P 500 surged as much as 3.7 percent in the morning, only to see the gains evaporate by midday. The index then bounced up and down before turning decisively higher after President Donald Trump pitched his ideas for a break on payroll taxes and other economic relief.

By the end of trading, the S&P 500 was up 4.9 percent. It erased three-fifths of Monday’s loss, which was the sharpest since 2008, when global authorities banded together to rescue the economy from the financial crisis.

While they won’t cure illnesses or get quarantined workers back into factories, spending and stimulus programs would put cash into the hands of households and businesses while health experts try to corral the virus. That could stave off or at least moderate a possible recession.