WASHINGTON — Senate Democrats rushed on Tuesday to nail down the details of a groundbreaking tax on billionaires’ wealth, part of an elaborate menu of tax increases to finance a significantly scaled-back bill that would strengthen the social safety net and address climate change.

Democrats’ plans to pay for about $1.5 trillion in social policy and climate spending could prove to be the most innovative components of the party’s top-priority domestic legislation, which was once envisioned as a transformative cradle-to-grave initiative to vault a stagnant working class into prosperity. Now, even as President Biden and his allies cut down the plan to ensure it can pass even with Democrats’ razor-thin edge in Congress, they are toiling to agree on new tax policies that could have far-reaching consequences.

Among them is a measure Senate Democrats presented on Tuesday that would impose a 15 percent minimum tax rate on corporations based on the profits they report to their shareholders, not what they show to the Internal Revenue Service.

The billionaires’ tax and the corporate minimum tax faced skepticism among House Democrats, who questioned their feasibility, and both were likely to face legal and constitutional challenges. For the first time, billionaires would face a tax on the unrealized gains in the value of their liquid assets, such as stocks, bonds and cash, which can grow for years as vast capital stores that can be borrowed off to live virtually income tax-free.

The courts would have to determine whether unrealized gains in wealth can be considered income under the 16th Amendment, which allows the federal government to tax income. And even if they passed legal muster, the measures were all but certain to spawn fresh tax avoidance efforts.

But with Senator Kyrsten Sinema, Democrat of Arizona, a crucial holdout on Mr. Biden’s plan, serving as a one-woman blockade against more conventional tax rate increases, Democrats appeared to have no choice but to turn to creative revenue measures.

“I’ve always felt that success was giving everybody in America the chance to get ahead, and what we’re dealing with here are flagrant loopholes in the tax code,” said Senator Ron Wyden, Democrat of Oregon and chairman of the Finance Committee. “They’re legal, but I’m going to close them.”

Democratic leaders hoped to unveil a final bill on Wednesday that could pass the House and Senate, but several sticking points remained.

Senator Joe Manchin III, Democrat of West Virginia, seemed to torpedo a plan that would require banks to provide the I.R.S. with more customer account information to help catch tax cheats, calling the idea “screwed up” and declaring it “cannot happen.” Dropping it would mean that Democrats would have to find another way to raise the hundreds of billions of dollars the provision was estimated to generate.

Senator Kirsten Gillibrand, Democrat of New York, was trying to line up support, including from Mr. Manchin, to beef up a federally paid family and medical leave provision that had been whittled down to just four weeks from 12.

Senator Raphael Warnock, Democrat of Georgia, threatened to withdraw his support for the bill if, as expected, it dropped a provision that would expand health coverage for the working poor in a dozen states like his that have refused to expand Medicaid under the Affordable Care Act.

Senator Bernie Sanders, independent of Vermont, was still furious over the refusal of a handful of Democrats to give Medicare broad powers to negotiate prescription drug prices.

But overall, liberal Democrats were trying to make their peace with a stripped-down bill that would turn a once-expansive vision for social transformation into a series of short-term measures — many of which would expire under a Republican Congress if history holds and the president’s party loses seats in next year’s midterms.

“I’d rather we put programs out there, and if people like them, then we should continue them as a government, and if for some reason they’re not popular, well, then that also helps make some determinations,” said Representative Mark Pocan, Democrat of Wisconsin and a leader of the progressive House Democrats.

Representative Pramila Jayapal, Democrat of Washington and the head of the Progressive Caucus, struck a pragmatic note: “Look, the thing is, we would have been done with a very different bill a month ago if we only needed 90 percent of us, but that’s not the case. We need 100 percent of us.”

Jen Psaki, the White House press secretary, acknowledged that the package would not contain everything that Mr. Biden wanted, but, she said, “The alternative to what is being negotiated is not the original package; it is nothing.”

Democratic leaders continued to frame the legislation as transformational, an heir to Franklin Roosevelt’s New Deal and Lyndon Johnson’s Great Society. They lumped in its $1.5 trillion in spending with the $1.9 trillion pandemic aid bill that passed last spring and a pending $1 trillion bipartisan infrastructure measure awaiting House passage.

“We’re hopeful, and we’re optimistic about the prospects of delivering something historic, transformative and bigger than one could possibly have imagined, on behalf of everyday Americans,” Representative Hakeem Jeffries of New York, chairman of the House Democratic Caucus, declared on Tuesday.

Ms. Jayapal said not all of the provisions had been truncated. Child care subsidies should last six years, and home and community-based health care assistance could stretch even longer.

But other measures have been cut. Two years of guaranteed community college were jettisoned. A broad path to citizenship for undocumented immigrants was knocked out by the Senate parliamentarian, so Democratic leaders were trying to win approval to grant temporary legal status to some undocumented immigrants.

An expansion of Medicare coverage to include dental, vision and hearing care appeared likely to be cut back, if not eliminated, so Mr. Sanders was pushing for a $1,000 debit card as a “bridge to a permanent program,” particularly for dental benefits. A permanent extension of the generous child tax credit created for a year in March’s pandemic relief bill was to be extended only another year.

That left the tax increases that Democrats were cobbling together on the fly as potentially the most far-reaching aspect of the plan. Ms. Sinema’s refusal to accept conventional tax rate increases has played into the hands of Senator Elizabeth Warren, Democrat of Massachusetts and a longtime proponent of creative measures to break through the tax avoidance strategies of the rich.

“These problems cannot be fixed by raising rates,” she said.

The corporate minimum tax, for instance, plays off Ms. Warren’s longstanding efforts to force companies to pay taxes off the profits they boast about to shareholders, rather than those they minimize for taxpaying purposes. The minimum tax unveiled on Tuesday was something of a substitute for initial efforts — blocked by Ms. Sinema — to raise the corporate income tax rate to at least 25 percent from 21 percent, still far lower than the 35 percent rate paid before President Donald J. Trump’s 2017 tax cut.

Under the plan, companies with at least $1 billion in profits — about 200 publicly traded corporations — would no longer be able to escape income taxation altogether. The 15 percent minimum tax would also bring the United States into compliance with the standard recently set by the Organization for Economic Cooperation and Development to try to root out tax havens.

Senate Finance Committee aides singled out Amazon, which over the last three years reported $45 billion in profits, including a record $20 billion last year, but paid an effective tax rate of 4.3 percent. In 2018, they said, Amazon did not pay anyfederal income tax. Senator Angus King, independent of Maine, estimated the minimum tax would raise $300 billion to $400 billion over 10 years.

Importantly, Ms. Sinema blessed it as “a common-sense step toward ensuring that highly profitable corporations — which sometimes can avoid the current corporate tax rate — pay a reasonable minimum corporate tax on their profits.”

The details of the billionaires’ tax were being hammered out on Tuesday night. Under the plan, Congress would impose a one-time tax on all the gains in value of tradable assets held by billionaires from the time they were initially purchased. That first hit would be huge, since men like Mark Zuckerberg of Facebook, Elon Musk of Tesla and Jeff Bezos of Amazon sit on vast shares of the companies they created, which initially had a value of zero.

After that, anyone with $1 billion in assets or who received $100 million in earnings for three consecutive years would face an annual tax on the gains in value of their publicly traded assets, whether or not they were sold.

House members continued to be leery.

“Do I like the politics of it? Yeah, I think it’s sensible,” Representative Richard E. Neal of Massachusetts, the chairman of the House Ways and Means Committee, said. “I think the implementation for the plan could be a bit more challenging.”

The problem may be in the Constitution, which gives Congress broad powers to impose taxes, but says “direct taxes” — a term without clear definition — should be apportioned among the states so that each state’s residents pay a share equal to the share of the state’s population.

The 16th Amendment clarified that income taxes do not have to be apportioned, and Mr. Wyden was careful to say his billionaires’ tax was a tax on income, not wealth: “You can’t have wealth without income,” he said.

But the 700 or so billionaires that would be hit with the tax would most likely disagree that unsold assets could be considered income, and they will have the wherewithal to take the matter to the Supreme Court, if necessary.

“Eventually, they run out of other people’s money, and then they come for you,” Mr. Musk complained on Twitter.

Reporting was contributed by Emily Cochrane, Alan Rappeport, Catie Edmondson and Zolan Kanno-Youngs.