WASHINGTON (AP) — The Democrats' idea for a new billionaires' tax  to help pay for President Joe Biden's social services and climate change plan has quickly run into criticism as too cumbersome, but party leaders insisted on Tuesday that a deal on Biden's big agenda was still within reach.

With the revenue side of the package deeply in flux, the Democrats continued to press for an agreement to show progress before the president departs later this week to global overseas summits.

House Speaker Nancy Pelosi told lawmakers during a caucus meeting they were on the verge of "something major, transformative, historic and bigger than anything else" ever attempted in Congress, according to a person who requested anonymity to share the private remarks.

Senate Majority Leader Chuck Schumer opened the Senate with a simple message: "We're working to get it done."

However, vast differences among Democrats remain over the basic contours of the sweeping proposal and how to pay for it. It's now estimated to total at least $1.75 trillion over 10 years, and could still be more.

From the White House, Press Secretary Jen Psaki said Biden's preference was still to have a deal in hand before departing, but she acknowledged that might not happen, forcing him to keep working on the package from afar.

"There are phones on Air Force One and also in Europe," Psaki told reporters.

In the meantime, she downplayed the billionaires' tax as among several tax and revenue options being discussed.

More lawmakers journeyed to the White House for negotiations in the afternoon and Psaki insisted talks were progressing: "We are almost there."

Resolving the revenue side is key as the Democrats scale back what had been a $3.5 trillion plan, insisting all the new spending will be fully paid for and not pile onto the debt. Biden vows any new taxes would hit only the wealthy, those earning more than $400,000 a year, or $450,000 for couples.

The White House had to rethink its tax strategy after one key Democrat, Sen. Kyrsten Sinema, D-Ariz., objected to her party's initial proposal to raise tax rates on wealthy Americans by undoing the Trump-era tax cuts on those earning beyond $400,000. Sinema also opposed lifting the 21% corporate tax rate. With a 50-50 Senate, Biden has no votes to spare in his party.

Instead, to win over Sinema and others, the White House has been floating a new idea of taxing the assets of billionaires and another that would require corporations to pay a 15% minimum tax, regardless of if they show any profits. Those both appear to be gaining traction with another pivotal Democrat, Sen. Joe Manchin, D-W.Va.,  who told reporters he supported new ways to ensure the wealthy to pay their "fair share."

Democrats on the Senate Finance Committee, led by Sen. Ron Wyden of Oregon, are prepared to roll out the tax revenue plan in a matter of days. It is likely to include other revenue-raising tax measures, though a plan to beef up the IRS to go after tax scofflaws faces new resistance from Manchin.

"Here's the heart of it: Americans read over the last few months that billionaires were paying little or no taxes for years on end," Wyden said at the Capitol.

The billionaires' tax is being modeled on a 2019 bill from Wyden to treat assets as income. Another idea, up to a 3% ultra-rich surtax, has been proposed by Sen. Elizabeth Warren, D-Mass.

Under Wyden's emerging plan, the billionaires' tax would hit the wealthiest of Americans, fewer than 1,000 people. It would require those with assets of more than $1 billion, or three-years consecutive income of $100 million, to pay taxes on the gains of stocks and other tradeable assets, rather than waiting until holdings are sold.

A similar billionaire's tax would be applied to non-tradeable assets, including real estate, but it would be deferred with the tax not assessed until the asset was sold.

Overall, the billionaires' tax rate has not been set, but it is expected to be at least the 20% capital gains rate. Democrats have said it could raise $200 billion in revenue that could help fund Biden's package over 10 years.

Senate Republican leader Mitch McConnell called it a "hare-brained scheme." Some Republicans indicated such a tax plan could be challenged in court.

But key fellow Democrats are also raising concerns, saying the idea of simply undoing the 2017 tax cuts by hiking top rates was more straightforward and transparent.

Under the House's bill  from the Ways and Means Committee, the top individual income tax rate would rise from 37% to 39.6%, on those earning more than $400,000, or $450,000 for couples. The corporate rate would increase from 21% to 26.5%. The bill also proposed a 3% surtax on wealthier Americans with adjusted income beyond $5 million a year.

The panel's chairman, Rep. Richard Neal, D-Mass., said that he told Wyden that the implementation of the senator's proposed billionaire's plan is "a bit more challenging."

Neal suggested that the House's proposal was not off the table. In fact, he said, "our plan looks better every day."

Once Democrats agree to the tax proposals, they can assess how much is funding available for Biden's overall package to expand health care, child care and other climate change programs.

Democrats were hoping Biden could cite major accomplishments to world leaders later this week. They are also facing an Oct. 31 deadline to pass a related $1 trillion bipartisan infrastructure package of roads, broadband and other public works before routine federal transportation funds expire Sunday.

After months of start-and-stop negotiations, disputes remain.

Among the unresolved provisions: plans to expand Medicare coverage with dental, vision and hearing aid benefits for seniors; child care assistance; free pre-kindergarten; a new program of four-weeks paid family leave; and a more limited plan than envisioned to lower prescription drug costs.

The climate change provisions may be resolving now that White House floated a new strategy to beef up clean energy incentives after Manchin rejected a more punitive approach.

Pelosi said she expected an agreement by week's end, paving the way for a House vote on the $1 trillion bipartisan infrastructure bill that stalled during deliberations on the broader Biden bill.

But Rep. Pramila Jayapal, D-Wash., the chair of the Congressional Progressive Caucus whose support will be crucial for both bills, said lawmakers want more than just a framework for Biden's plan before they give their votes for the smaller infrastructure package.

"We want to vote on both bills at the same time," Jayapal told The Associated Press.

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Associated Press writers Farnoush Amiri, Hope Yen and Colleen Long contributed to this report.

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This story has been corrected to show Rep. Richard Neal is from Massachusetts, not New Jersey.