Sixty percent responded that they knew someone who had tested positive.
The poll quizzed 803 registered state voters between April 19 and 23.
It found that 87 percent were in favor of Governor Andrew Cuomo's decision to extend New York's lockdown until at least May 15.
Cuomo said on Sunday that manufacturing and construction may start in the least-affected areas of New York state after May 15 as part of a phased reopening.
President Donald Trump, bracing for November elections, is impatient to resume business but some 56 percent of people polled said they were not confident America "will be back to normal anytime soon."
Several states have seen protests against stay-at-home orders and Georgia has allowed thousands of businesses to resume operations, against the advice of health experts.
Eighty-four percent of voters polled by Siena said they approved of Democrat Cuomo's handling of the virus outbreak.
Only 34 percent in the traditionally Democratic state approved of Trump's handling of the crisis, the survey found.