Treasury Secretary Steven Mnuchin arrives at the Capitol for a closed-door meeting with Senate Majority Leader Mitch McConnell, R-Ky, as they struggle to get a tax code overhaul, in Washington, Tuesday, Sept. 12, 2017. The as-yet-undrafted bill to overhaul the tax code is the top priority for Trump and Republicans after the collapse of their effort to dismantle Barack Obama’s health care law. (AP Photo/J. Scott Applewhite)

WASHINGTON (AP) — Senate Republicans are struggling with how many billions of dollars President Donald Trump’s tax code overhaul will add to the deficit as they work on a GOP budget plan that’s a prerequisite to any far-reaching change in the nation’s tax system.

Trump had dinner Tuesday with a group of Republican and Democratic senators to talk taxes, after Senate Majority Leader Mitch McConnell and GOP members of the Budget Committee met with two top Trump administration officials to make progress on forging the budget plan, which is required to stave off potential Democratic blocking tactics and pass the subsequent tax bill with just GOP votes.

The as-yet-undrafted bill to overhaul the tax code is the top priority for Trump and Republicans after the collapse of their effort to dismantle Barack Obama’s health care law. Trump’s top economic adviser, Gary Cohn, and Treasury Secretary Steven Mnuchin met with McConnell, R-Ky., and budget panel members.

“From my standpoint, let’s set ourselves up for success on tax reform,” Sen. Ron Johnson, R-Wis., a member of the committee, said before the meeting.

The meeting ended in late afternoon without specific proposed numbers for the size of the budget coming forward. Not wanting to show disappointment, participants stressed that it was intended to be preliminary.

Finance Committee Chairman Sen. Orrin Hatch said afterward that the group, which discussed the broad outlines of the deficit trade-off for a new tax bill, had not reached an agreement. Hatch, R-Utah, said he expected more information to come soon.

Mnuchin signaled ahead of the meeting that the administration would be open to changes sought by lawmakers to improve the chances for passage of a tax overhaul this year. In an interview with CNBC, Mnuchin also said the administration would “absolutely” consider making tax cuts retroactive to the start of this year if overhaul legislation didn’t pass until 2018.

In addition, the administration would consider including an infrastructure spending bill as part of the tax legislation, Mnuchin said.

“This is a pass-fail exercise,” he said, indicating that the critical goal was to enact legislation. “Passing tax reform, which hasn’t been done in 31 years, that is a win,” he said.

Capitol Hill Republicans have promised that the tax rewrite will be “revenue neutral” and not add to the nation’s $20 trillion-plus debt, but they are in fact counting on budget maneuvers to find hundreds of billions of dollars to help maximize cuts to corporate and individual tax rates. For starters, they are going to assume the tax legislation will mean higher economic growth and greater future tax revenues.

Underscoring the president’s desire for tax legislation, Trump hosted a bipartisan group of senators for dinner at the White House, including a trio of moderate Democrats from states Trump won last November and whose votes he’d like to have on a tax bill.

Democratic Sens. Joe Manchin of West Virginia, Heidi Heitkamp of North Dakota and Joe Donnelly of Indiana were joined at dinner by Republican Sens. John Thune of North Dakota, Pat Toomey of Pennsylvania and Hatch, the White House said.

“I had a productive conversation with @POTUS @realDonaldTrump about ways we can work together in a bipartisan manner on tax reform,” Manchin tweeted after the dinner, along with a photo of himself and the president. He said in a statement that he would “continue to fight for a simpler tax code that lowers rates for West Virginians,” but said that must be done “without adding to our staggering debt.”

Heitkamp said she welcomed any chance “to talk with the president about issues important to North Dakota” and was looking forward to reviewing Trump’s plans in more detail.

“It’s encouraging that this meeting included Republican and Democratic senators, as I’ve long said I want to work with those on both sides of the aisle on a comprehensive, permanent tax reform plan that works for North Dakota workers and retirees and helps grow the economy, and I hope these bipartisan discussions continue,” she said.

Manchin, Heitkamp and Donnelly are the only Democratic senators who did not sign a letter addressed to Republican leaders and Trump that said the Democratic caucus would not support a tax overhaul that cuts taxes for the “top 1 percent” or adds to the government’s $20 trillion debt.

The White House, meanwhile, said the president “looks forward to continuing to work with members from both parties to grow the economy, provide tax relief and look for real solutions.”

“When members of different parties sit down together for friendly conversation about the legislative agenda, after not doing so for 8 years, it certainly is progress,” Press Secretary Sarah Huckabee Sanders said.

House action has been held up by a battle between moderates and conservatives over whether to pair spending cuts with the filibuster-proof tax measure. Senate action has been on hold while the House struggles.

An impasse could doom the tax overhaul effort.

GOP aides say the Senate panel is also likely to reject a House plan to link $200 billion in spending cuts to the tax legislation — a key demand of House conservatives.

The momentum toward deficit-financed tax cuts runs counter to the longtime promises from top Capitol Hill leaders that this year’s effort to rewrite the tax code wouldn’t add to the government’s $20 trillion-plus national debt. And it sets up a scenario in which many of the promised new tax rates would expire after 10 years. That’s because of the Senate’s arcane rules.

On the budget panel, Sen. Bob Corker, R-Tenn., is hoping to limit the deficit cost of the tax effort, while Toomey is on the other end of the spectrum favoring more robust deficit-financed tax cuts. GOP leaders have asked them to try to craft an agreement among the 12 budget panel Republicans. Any Republican defection on the budget plan would deadlock the narrowly divided committee.