Senate Finance Committee Chairman Orrin Hatch Orrin Grant HatchBottom line Bottom line Senate GOP divided over whether they'd fill Supreme Court vacancy MORE (R-Utah) said Wednesday that it's "highly unlikely" the Senate would vote by the end of the year on a new tax cut proposal teased by President Trump Donald John TrumpBiden says voters should choose who nominates Supreme Court justice Trump, Biden will not shake hands at first debate due to COVID-19 Pelosi: Trump Supreme Court pick 'threatens' Affordable Care Act MORE.

"I think it can but it would take a real monumental effort to get it through, no question. But it's always taken a monumental effort, and a lot depends on the political climate and, as you know, I've seen miracles happen before," Hatch said, when asked if the floated tax proposal could pass.

Pressed if thought there could be a vote during the lame-duck session, Hatch added: "You can't count out the Congress. …[But] it would be highly unlikely."

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Trump said earlier this week that he would push for a vote on a second round of tax cuts after the midterm elections that will include a 10-percent reduction for middle-class Americans.

"We're doing it now for middle-income people. This is not for business, this is for [the] middle," Trump told reporters at the White House, adding that "we'll do the vote after the election."

As chairman of the Senate Finance panel, Hatch, who is retiring after this Congress, would be responsible for guiding an tax bill through the chamber this year. He said he has not spoken to Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellHawley warns Schumer to steer clear of Catholic-based criticisms of Barrett Senate GOP set to vote on Trump's Supreme Court pick before election Harris slams Trump's Supreme Court pick as an attempt to 'destroy the Affordable Care Act' MORE (R-Ky.), who would be responsible for scheduling floor time, about a potential vote.

Trump's second tax cut proposal, following a reform bill he signed in December, appeared to catch both Congress and even his own aides off guard when he initially suggested it would come up before the November election.

Congress is currently out of session until Nov. 13. When they return to Washington, they still need to resolve funding for parts of the government — including a looming fight over Trump's U.S.-Mexico border well.

House Ways and Means Committee Chairman Kevin Brady Kevin Patrick BradyBusinesses, states pass on Trump payroll tax deferral Trump order on drug prices faces long road to finish line On The Money: US deficit hits trillion amid pandemic | McConnell: Chance for relief deal 'doesn't look that good' | House employees won't have payroll taxes deferred MORE (R-Texas) said Tuesday that the House would work with Trump on a new round of tax cuts if Republicans keep control of both chambers in the midterms next month.

Neither Brady nor Trump discussed how to finance the tax cuts. The nonpartisan Congressional Budget Office projected that the 2017 GOP law would add $1.9 trillion to the deficit over a decade.

Hatch, speaking with reporters in the Dirksen Senate Office Building, declined to comment on the specifics of the potential proposal, saying he has a "general knowledge" but needed to "get into more details" before talking about it.

He declined to specifically say if he had spoken with Trump about the proposal, noting that they "talk all the time." Asked if there is currently a tax cut proposal on the table, Hatch added, "I think there will be."

"It will come right to me," he told reporters, "so I'll be doing my best not to mess it up."