President Biden promised on Tuesday to continue pushing to expand child care subsidies, early education and paid medical leave, agenda items left unfulfilled during his three and a half years in the White House.

The promises, made in a speech to a crowd of enthusiastic caregivers at Union Station in Washington, were meant to reassure Democratic voters that he would use a second term to fight against Republicans who blocked his ambitious measures.

He called for 12 weeks of paid family or medical leave, large investments in preschool for 4-year-olds, the extension of a child tax credit to help working families, and investments to give families access to high-quality child care for $10 per day.

“All this helps families and it grows the economy, grows the economy,” he told the crowd to applause. “And we can afford to do it. We can’t afford not to do it.”

Mr. Biden pursued many of his care economy proposals earlier in his presidency. His Build Back Better plan in 2021 originally included big investments in preschool and health care workers. But most of those proposals were dropped during heated negotiations with some conservative Democrats in the Senate.

Now, as the election battle with former President Donald J. Trump intensifies, Mr. Biden is hoping that supporters of those ideas will want him to have another four years to pass them into law.

The president included his new proposals in his budget for next year, an election year document that members of both parties acknowledge is dead on arrival on Capitol Hill. For Mr. Biden, it is an aspirational document meant to lay out his priorities if he were re-elected.

In the speech, Mr. Biden excoriated Republicans, who have opposed many of the proposals as too costly at a time when the nation has been struggling with mounting debt. He accused Republicans of proposing their own budget that “cuts caregiving programs by a third” and aims to “terminate the Affordable Care Act.”

Mr. Biden concluded his remarks on Tuesday with a message to the care workers in the audience: “As your president I’m here with a simple message. I give you my word: I have your back.”