“We’re going to get a lot done,” President Biden said, as Senate Democrats began drafting the details on a social and environmental bill that could yield transformative change.WASHINGTON — 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 still far from reality, but the details that top Democrats have coalesced around are far-reaching. Prekindergarten would be universal for all 3- and 4-year-olds, two years of community college would be free, utilities would be required to produce a set amount of clean energy, and prescription drug prices would be lowered. 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 crucial moderate lawmakers had yet to say whether they would accept the proposal, with a majority of policy details left to resolve.Mr. Biden’s message to the senators on Wednesday, said Senator Richard Blumenthal of Connecticut, was “be unified, strong, big and courageous.”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 chamber leaves for the August recess — a complex and politically tricky task in a 50-50 Senate. The narrowly divided House would also have to pass the budget blueprint before both chambers begin tackling the detailed legislation.Speaker Nancy Pelosi, who must ultimately get the package through the House, embraced the deal, telling Democrats in a letter on Wednesday, “This budget agreement is a victory for the American people, making historic, once-in-a-generation progress for families across the nation.”The outline includes large swaths of Mr. Biden’s $4 trillion economic agenda. It wraps in every major category from his American Families Plan, including investments in child care, paid leave and education, and expanded tax credits that this week will begin providing a monthly check to most families with children.“I think we’re going to get a lot done,” Mr. Biden told reporters as he left his first in-person lunch with the Democratic caucus as president.Nodding to budget constraints, party leaders conceded that many of the programs included in their plan — including the tax credits — could be temporary, leaving a future Congress to decide whether to extend them further.The proposal also includes some measures that go beyond what Mr. Biden has called for, like expanding Medicare to cover dental, vision and hearing benefits. Democratic leaders left it to the Senate Finance Committee to decide whether to include reducing the eligibility age for Medicare to 60, a priority of Senator Bernie Sanders of Vermont, the Budget Committee chairman.The resolution would also create what would effectively be a tax on imports from countries with high levels of greenhouse gas emissions. That could violate Mr. Biden’s pledge not to raise taxes on Americans earning less than $400,000 a year if the tax is imposed on products that typical consumers buy, such as electronics from China.Democrats on Mr. Sanders’s committee must produce a budget resolution in the coming days that includes so-called reconciliation instructions to other Senate committees, which in turn will draft legislation detailing how the $3.5 trillion would be spent — and how taxes would be raised to pay for it.That would pave the way for Democrats to produce a reconciliation bill this fall that would be shielded from a filibuster, allowing them to circumvent Republican opposition but requiring all 50 of their members — and a majority in the narrowly divided House — to pass it.“In some cases, it doesn’t provide all the funding that I would like to do right now,” Mr. Sanders said. “But given the fact that we have 50 members, and that compromises have got to be made, I think this is a very, very significant step forward.”He added: “If you’re asking me at the end of the day, do I think we’re going to pass this? I do.”A neighborhood in Austin, Texas, where many homes have solar panels. The blueprint of the legislation includes clean energy provisions and other social programs.Tamir Kalifa for The New York TimesAt the private lunch, Senator Chuck Schumer of New York, the majority leader, outlined the proposal and the directives it would lay out.Democrats included the creation of a civilian climate corps to add jobs to address climate change and conservation, and to provide for child care, home care and housing investments. They are also expected to try to include a path to citizenship for some undocumented immigrants and address labor protections.Democrats would also extend expanded subsidies for Americans buying health insurance through the Affordable Care Act that were included in the broad pandemic aid law that Mr. Biden signed this year.Huge investments would go to renewable energy and a transformed electrical system to move the U.S. economy away from oil, natural gas and coal to wind, solar and other renewable sources. The budget blueprint is to include a clean energy standard, which would mandate the production of electricity driven by renewable sources and bolster tax incentives for the purchase of electric cars and trucks.To fully finance the bill, it is expected to include higher taxes on overseas corporate activities to alleviate incentives for sending profits overseas, higher capital gains rates for the wealthy, higher taxes on large inheritances and stronger tax law enforcement.Senator Ron Wyden of Oregon, the chairman of the Finance Committee, said on Wednesday that he was also preparing to overhaul a deduction for companies not organized as corporations, like many small businesses and law firms — created by the 2017 Republican tax law — in order to cut taxes from small businesses but raise additional revenues from wealthy business owners.Specific provisions will have to pass muster with the strict budgetary rules that govern the reconciliation process, which require that provisions affect spending and taxation, not just lay out new policies. The Senate parliamentarian could force Democrats to overhaul or outright jettison the clean energy standard, the provision that climate activists and many scientists most desire, as well as the immigration and labor provisions, among others.Moderate Democrats, who had balked at a progressive push to spend as much as $6 trillion on Mr. Biden’s entire economic agenda, largely declined to weigh in on the blueprint until they saw detailed legislation, saying they needed to evaluate more than an overall spending number.“We’ve got to get more meat on the bones for me,” Senator Jon Tester, Democrat of Montana, told reporters, though he added that he would ultimately vote for the budget blueprint. “I’ve got to get more information on what’s in it.”The size of the package could be shaped by the success or failure of the bipartisan infrastructure plan, which would devote nearly $600 billion in new spending to roads, bridges, tunnels, transit and broadband. The group of lawmakers negotiating that package has yet to release legislative text as they haggle over the details of how to structure and pay for the plan.“I want to be able to tell people in South Carolina: I’m for this, I’m not for that,” said Senator Lindsey Graham of South Carolina, the top Republican on the Senate Budget Committee.Stefani Reynolds for The New York TimesIf Republicans cannot deliver enough votes to move the package past a filibuster, Democrats could simply fold physical infrastructure spending into their reconciliation plan and take away any chance for Republicans to shape it, said Senator Rob Portman, Republican of Ohio and one of the negotiators of the bipartisan bill.“If we don’t pass infrastructure, they’re going to put even more infrastructure in than we have and worse policies,” said Mr. Portman, who fielded skepticism from his colleagues at a private Republican lunch on Tuesday. Some Republicans had hoped that a bipartisan accord on physical infrastructure projects would siphon momentum from a multitrillion-dollar reconciliation package. Instead, it appears very much on track, and it may intensify the pressure on Republicans to come to terms on a bipartisan package, even if they fiercely oppose the rest of the Democrats’ agenda.“I want to be able to tell people in South Carolina: I’m for this, I’m not for that,” said Senator Lindsey Graham of South Carolina, the top Republican on the Budget Committee and a peripheral presence in the bipartisan talks.He added that the lengthy floor debate over the blueprint would allow Republicans to “ferociously attack it, to have amendments that draw the distinctions between the parties, to scream to high heaven that this is not infrastructure.”Senator Joe Manchin III of West Virginia, a moderate Democrat, said he looked “forward to reviewing this agreement” but was also interested in how the programs would be financed.Sarahbeth Maney/The New York TimesSenator Joe Manchin III of West Virginia, the centrist Democrat whose support might be determinative, told reporters after lunch with the president that he had concerns about some of the climate language. But he did not rule out supporting the budget proposal or the subsequent package. Senator Kyrsten Sinema, Democrat of Arizona and another key moderate, also hung back on Wednesday.Still, the $3.5 trillion package had plenty in it to appeal to senior Democrats who were eager to use it to advance their longtime priorities. For Senator Patty Murray of Washington, the chairwoman of the Health, Education, Labor and Pensions Committee, it was an extension of a more generous child tax credit, as well as subsidies for child care, prekindergarten and paid family leave.For Mr. Sanders, it was the Medicare and climate provisions.“Finally, we are going to have America in the position of leading the world in combating climate change,” he said.Mr. Tester said the need for school construction was so high that trillions could go to that alone.“The plan is a strong first step,” said Senator Elizabeth Warren, Democrat of Massachusetts, adding that she was focused on funding universal child care. “We’re slicing up the money now to find the right ways to make that happen.”The budget measure is expected to include language prohibiting tax increases on small businesses, farms and people making less than $400,000, fulfilling a promise Mr. Biden has maintained throughout the negotiations. Asked on Wednesday whether the proposed carbon tariff would violate that pledge, Mr. Wyden replied, “We’ve not heard that argument.”Lisa Friedman More