President Biden took his bid for a second term on the road on Friday, effectively opening the general election campaign with a strongly populist pitch and an aggressive attack on his Republican challenger, former President Donald J. Trump.

Kicking off a monthlong set of barnstorming trips mainly to swing states, Mr. Biden reprised the themes of his State of the Union address at a rally in Wallingford, Pa., as he sought to capitalize on his robust nationally televised performance and galvanize Democrats who have been anxious about his age and poor poll numbers.

Mr. Biden made clear that his regular targets during this re-election bid would be billionaires, corporations, pharmaceutical companies, banks, credit card companies and even potato chip makers. All of them, in his telling, are out to gouge consumers and duck their fair share of taxes. But his favorite villain in his election-year narrative will still be Mr. Trump, his opponent from 2020 now in a rematch set by this week’s Super Tuesday primaries.

“Donald Trump and the MAGA Republicans are trying to take away our freedoms,” Mr. Biden told a crowd of cheering Democrats in a school gymnasium, this time not shying away from citing his challenger by name, unlike the night before. “That’s not an exaggeration. But guess what? We will not let him.”

Mr. Biden seemed delighted by the reviews of his State of the Union address, which allies hope will jump-start his campaign after months of Democratic uncertainty about his prospects. “I got my usual warm reception from Congresswoman Marjorie Taylor Greene,” he joked, referring to the Georgia Republican who had heckled and jeered him.

He was so pumped up after the speech, he said, that he stayed up until 2 a.m. and checked out the Fox News coverage. Unsurprisingly, he disagreed with the conservative network’s take that his economic policies would “ruin America,” as he summarized it. “We have the strongest economy in the world right now,” he said.