President Biden is discovering that passing one of the most ambitious legislative agendas in recent American history may have been the easy part. Persuading Americans that he deserves a second term may be far more difficult.

Confronting low approval ratings and a neck-and-neck race against former President Donald J. Trump, Mr. Biden is now racing to tell voters about his accomplishments, in ways big and small.

Road signs that promote his legislation are going up at construction projects financed by his $1 trillion infrastructure bill and at factories where jobs are being created by his $280 billion CHIPS and Science Act. Mr. Biden has affixed his name to emails telling Americans with student debt that their loans were being forgiven. And he is traveling to battleground states to sit down with voters who have benefited from his policies.

Democrats traditionally have been “the party of the abstract, and we need to be the party that humanizes things,” said Gov. Phil Murphy of New Jersey, a Biden ally who believes the president has the skill set to do just that. “He personally is so good at this, putting his arm — figuratively and literally — around the American people and saying, ‘Hey, listen, I feel your pain.’”

But Mr. Biden faces a host of challenges in reaping the credit that he feels he deserves as he seeks re-election to the White House.

Polling shows that a majority of Americans disapprove of his job performance. Many Americans say they benefited more from the policies of Mr. Trump. Most concerning for Mr. Biden, his support remains underwhelming among key parts of the Democratic coalition, including Black and Hispanic Americans and younger voters — the people many of his efforts were designed to help.