President Biden and congressional Democrats vowed on Wednesday to push through a $3.5 trillion budget blueprint to vastly expand social and environmental programs by extending the reach of education and health care, taxing the rich and tackling the warming of the planet.

The legislation is far from passage, but top Democrats have agreed on working to include several far-reaching details. They include universal prekindergarten for all 3- and 4-year-olds, two years of free community college, clean energy requirements for utilities and lower prescription drug prices. Medicare benefits would be expanded, and green cards would be extended to some undocumented immigrants.

At a closed-door luncheon in the Capitol, Mr. Biden rallied Democrats and the independents aligned with them to embrace the plan, which would require every single one of their votes to move forward over united Republican opposition. But several moderate lawmakers who are crucial to the plan’s success had yet to say whether they would accept the proposal.

Mr. Biden’s message was “be unified, strong, big and courageous,” Senator Richard Blumenthal of Connecticut said.

Senate Democratic leaders have said they aim to pass both the budget blueprint and a narrower, bipartisan infrastructure plan that is still being written before the August recess. That will be a politically tricky task in an evenly split Senate. The narrowly divided House would also have to pass the blueprint before both chambers tackle the details.