There have been so many bad polls for President Biden that his playbook for them by now is well worn.

First, dismiss the polling industry as inherently broken. Next, argue about the metrics. Finally, remind supporters of how many months remain before Election Day and highlight the structural and financial advantages the Biden campaign has built while former President Donald J. Trump is tied up in court.

In the weekend before Monday’s poll from The New York Times, Siena College and The Philadelphia Inquirer found Mr. Trump leading Mr. Biden in five of the six battleground states surveyed, Mr. Biden traveled to the West Coast. Speaking to donors in San Francisco and the Seattle area, he made the case that they should ignore the polling — especially if it looks bad for him.

“People are engaged, no matter what the polling data says,” Mr. Biden said Friday in Seattle. “It’s awful hard to judge the polls these days because they’re so difficult to take.”

The president’s comments suggest that his internal polling data mirrors that of The Times and Siena College, which found a sizable gap between registered and likely voters.

“We run strongest among likely voters in the polling data,” he told supporters at a campaign fund-raiser on Saturday in Medina, Wash., an upscale suburb of Seattle. “That’s a good sign. And while the national polls basically have us registered voters up by four, likely voters we’re up by more.”

And then there’s Mr. Biden’s campaign, which has opened 150 offices with more than 500 staff members across the battleground states. Those employees, along with what is expected to be a $2 billion advertising campaign by the end of this cycle, are aiming to turn the November election into a referendum not on Mr. Biden, but on his predecessor, by reminding voters about Mr. Trump’s record on abortion and democracy.

Part of Mr. Biden’s problem, his aides and advisers have said for nearly a year, is that too many voters have forgotten the most alarming parts of the Trump years. Mr. Biden’s campaign aides — and the president himself — have gone to great lengths to try to highlight Mr. Trump’s part in limiting abortion rights and his public statements about democracy and health care.

“Trump is trying to make the country forget how dark and unsettling things were when he was president,” Mr. Biden said at the Seattle fund-raiser. “But we’re never going to forget.”