When the country catches a cold, Nevada gets the flu. That’s the common wisdom for the economy in the state, which is heavily dependent on tourism and suffered more than any other from pandemic lockdowns.

The same idea could apply to President Biden’s polling numbers. New surveys by The New York Times, The Philadelphia Inquirer and Siena College published on Monday showed Mr. Biden trailing former President Donald J. Trump in nearly every battleground state, but he appeared to be in the roughest shape in Nevada, where he was down by 12 percentage points among registered voters.

In Nevada, two of Mr. Biden’s biggest problems — his weakness with Hispanic voters and pessimism over his handling of the economy — seem magnified. With the state’s economy slow to recover from the pandemic, 61 percent of registered voters in the poll said they trusted Mr. Trump to do a better job handling the economy, compared with 32 percent who trusted Mr. Biden. And Hispanic voters, whose support was crucial to Mr. Biden in 2020, said they preferred Mr. Trump to him by nine points in a head-to-head matchup.

Democrats in the state acknowledge the challenge ahead of them. But they note that Nevada is a notoriously difficult state to survey, with polls in recent cycles underestimating Democratic candidates who went on to win. A Republican presidential candidate has not won Nevada since 2004.

“Like everything in organizing, it’s not going to be easy,” Ted Pappageorge, the secretary-treasurer of the state’s 60,000-member Culinary Workers Union, a key part of the Democratic coalition in Nevada, said in a statement. “But we do have a plan to win and we think that voters, when confronted with receipts of Trump and his chaos, and Biden and his leadership and what he has done for working people, will make the right decision.”

Other Nevada polls also show Mr. Trump ahead of Mr. Biden, although by a smaller margin.

Few political operatives expect anything other than a close race in the state in November, and certainly not a double-digit blowout; even Republicans expressed surprise at the size of Mr. Trump’s polling lead. Mr. Biden won Nevada by about 2.5 points in 2020, capitalizing on the powerful organizational advantage that Democrats have long enjoyed in the state. And Democrats said their political machine — made up of members of the Culinary Union and party loyalists assembled by Harry Reid, the former Senate majority leader who died in 2021 — was not yet fully active.