Neither the Times nor Siena broke out results by day, but pollster and journalist Nate Cohn wrote on the Times’ website that data provided “modest evidence of a shift in favor of … Biden in interviews on Friday,” including in a still-ongoing survey in Arizona that will be released later.

In Florida, Biden’s lead is built on advantages with traditional Democratic constituencies, but the Democrat also runs strong among groups Republicans have typically won. Among voters under age 30, Biden leads Trump, 62 percent to 25 percent. But he is also running neck-and-neck among seniors in the retirement haven: 47 percent for Biden, and 45 percent for Trump.

In 2016 in Florida, Hillary Clinton won voters under 30 by 18 points, and Trump won seniors by 17 points, according to exit polls.

Biden also posts a solid lead among Latino voters, 58 percent to 34 percent. That’s despite concerted efforts by the Trump campaign to appeal to Florida Latinos, especially voters with Cuban and South American ancestry. Clinton won Florida Latinos, 62 percent to 35 percent, according to the exit poll.

And Biden is also peeling away enough Republicans and independents to build his lead. He is winning Democrats, 93 percent to 3 percent, but also has a 12-point lead with independents and captures 11 percent of Republicans.

The results were similar in Pennsylvania, where Biden leads by 13 points among independents and is winning 11 percent of the Republican vote.

Biden is also racking up huge margins in the suburbs of Pennsylvania, thanks to his support among upscale white voters. White voters with college degrees back Biden, 60 percent to 31 percent, while whites without degrees go for Trump by a 24-point margin, 58 percent to 34 percent.

That gives Biden a nearly two-to-one advantage in the traditionally competitive Philadelphia suburbs, 60 percent to 32 percent. Clinton won Philadelphia suburbs 55 percent to 42 percent, according to exit polls.

Biden has a slim lead in the battleground Northeast part of the commonwealth, 48 percent to 40 percent.

The surveys suggest Trump did little in the debate to boost his flagging candidacy. Trump flouted the agreed-upon rules and frequently interrupted Biden, and also failed to condemn an extreme, right-wing group.

Majorities in both states, 53 percent in Florida and 52 percent in Pennsylvania, “strongly disapprove” of the way the president conducted himself on Tuesday night, and roughly two-in-three voters disapprove of his debate performance overall. Meanwhile, slim majorities in both states approved of Biden’s debate performance.

The Florida poll surveyed 710 likely voters and has a margin of error of plus or minus 4.2 percentage points. In Pennsylvania, 706 likely voters were surveyed, and results carry a margin of error of plus or minus 4.1 percentage points.