With the votes apparently lined up to pass a 2018 budget this week, President Trump began pressing his case Wednesday with key senators who will write a tax-code overhaul later this year.

President Donald Trump, center, speaks during a meeting with members of the Senate Finance Committee and members of the President's economic team in the Cabinet Room of the White House in Washington, Wednesday, Oct. 18, 2017. Trump is joined by, from left, Sen. Tim Scott, R-S.C., White House chief economic director Gary Cohn, Sen. Claire McCaskill, D-Mo., and Senate Finance Committee Chairman Sen. Orrin Hatch, R-Utah. (AP Photo/Susan Walsh)

"This is a once-in-a-lifetime opportunity in my opinion," Trump said before a private meeting with Democrats and Republicans on the Senate Finance Committee. "I have had people on both sides, that I promise not to mention ... but a lot of people are liking this very much and I think we'll have tremendous support."

Republicans and Democrats said after the meeting that senators aired their stances on how tax reform should work, but there was no indication of actual progress on a bipartisan effort.

Away from the meeting, Democrats had the tax plan in their crosshairs as they prepared for a series of budget-related votes.

"Our Republican friends are trying to hide it, they don't want to discuss what's in the bill," Senate Minority Leader Chuck Schumer, D-N.Y., said at a news conference Wednesday. "You ever hear them talk about cutting Medicare or Medicaid? Ever hear them talk about tax breaks for the wealthiest people in America? They don't mention it. They don't want people to know."

Passage of the budget is a key step toward unveiling an actual tax bill, because the budget includes language known as reconciliation instructions that would prevent a Democratic filibuster on a tax bill. Filibusters require 60 votes to shut down, but reconciliation would allow the Senate to pass a tax bill with 51 votes. There are 52 Republicans in the Senate.

But it also gives a sense of what the majority Republicans want spending to be, and the tax bill is built around those instructions.

Schumer also touted a study by the liberal Center for American Progress that estimated how much Trump himself and millionaires in his Cabinet would save from the Republican tax plan's provisions to eliminate the estate tax and lower the top rate for so-called "pass through" income to 25 percent.

"What happened with health care is what's going to happen with their tax bill," Schumer said. "The American people learned over a period of months... how bad this bill was and they turned against it, and then the Republicans couldn't pass it."

There is no tax bill yet, and the budget resolution which must still be passed by both houses of Congress is not a binding law. As a result, people on both sides can cite figures based on studies of what might happen.

Sen. Bernie Sanders of Vermont, the top Democrat on the budget committee, said the Republican-crafted spending framework calls for $5.1 trillion in spending cuts during the coming decade, including $1 trillion from Medicare and $470 billion from Medicaid.

Those cuts would have to happen from other legislation passed in the future, however. Sanders also pointed to a preliminary study by the nonpartisan Tax Policy Center to decry the distribution of tax cuts.

"This is a budget that would provide 80 percent of its tax breaks to the top 1 percent," Sanders said at a news conference Tuesday. "This is a budget that must be defeated."

Trump, meanwhile, said the plan would benefit to working families by doubling the amount of income that could be earned before any income tax is owed and increasing the child tax credit. He also said his Council of Economic Advisers estimated the average family would get a $4,000 bump as a result of lowering the top corporate tax rate and encouraging companies to bring back money they have held with overseas subsidiaries.

Republican senators who have said they might not support the final tax bill said they were supporting the budget resolution to keep the process moving. Sen. Bob Corker of Tennessee, for example, said he would not back the tax bill that increases the deficit. 

The Senate budget resolution would allow a tax bill to reduce revenues by as much as $1.5 trillion over the coming decade, but it also anticipates economic growth would make up some of that difference, a process known as dynamic scoring that Democrats have said is just wishful thinking.

A House version of the budget approved last week would require tax cuts to be offset by spending cuts, including cuts to entitlement programs. The two competing measures will have to go to a conference committee and a compromise must be approved again in each house before the House Ways and Means Committee would being to consider a tax bill.  

Senators leaving the meeting with Trump said it was cordial, but differences remained.

Sen. Pat Toomey, R-Pa., said there were "areas of overlap" discussed.

Sen. John Thune, R-S.D., said there was an element of "kumbaya" in the room, with senators all saying they wanted to work together to deliver lower taxes for the middle class. But he said that for Democrats to join negotiations, they will have to back off a demand not to use dynamic scoring.

"To get the growth that we want to get out of it, to get the rates down where we think they need to go, we're going to assume a small amount of dynamic scoring. I think it's a reasonable amount," said Thune.

Sen. Ron Wyden of Oregon, the top Democrat on the committee, said the meeting was productive because Trump got to hear that Democrats agree the tax code needs changing and that middle class deserves help.

But Wyden said the framework for taxes Trump and Republican leaders released last month includes specific benefits for the rich, including repealing the estate tax, which only estates worth more than $5 million, and bringing the top bracket down from 39.6 percent to 35 percent.

Wyden said that when Democrats raise concerns about those in the middle class who might be hurt, including with high state and local taxes who could lose the ability to deduct them from federal taxes, there are only vague assurances they will be protected in the bill.

"There is a big gap between the rhetoric and the reality of what is in the Trump plan and that is what I focused on," Wyden said. "When the president says again and again, 'I'm for helping the middle class, I'm not for helping the wealthy, I'm not for hurting Social Security Medicare and Medicaid', and then you look at the piece of paper that's on offer, and you see this Grand Canyon-sized gap."

Sen. Claire McCaskill, a Democrat from the Missouri — which Trump won overwhelmingly last year — who was seated next to Trump at the meeting and declined to characterize it afterward.

Asked if she thought it was hopeful, she said;  "I think the president would really like to have some Democrats engaged."

Contributing: David M. Jackson and Heidi Przybyla