Senate Majority Leader Mitch McConnell, R-Ky., told "The Story" Wednesday night that it would be "a mistake" to include funding for a new FBI headquarters building in the next round of coronavirus relief legislation after President Trump said Republicans who opposed the idea should “go back to school.”

However, McConnell reminded host Martha MacCallum, "in the Democratic bill over in the House, they've got a tax cut for rich people in blue states. That's not related to COVID-19 either."

McConnell was referring to a provision in the House-passed HEROES Act that calls for the restoration of the State and Local Tax (SALT) deduction.

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"I think whatever we finally agree on, all of these items -- whether it's the FBI building, whether its a tax cut for high-income people in blue states -- ought to come out," he said, emphasizing that "the bill ought to be narrowly crafted to deal only with the coronavirus."

Despite his opposition to Trump's FBI headquarters push, McConnell said he is "consulting with the White House and trying to get on the same page as much as we can."

Lawmakers have begun negotiating the terms of the newest stimulus package, just days before Americans will lose their boosted unemployment benefits from the federal government and, for many, their rent will come due.

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Democrats have said that the $1 trillion GOP proposal, which is controversial within even the Republican caucus and which President Trump called "semi-irrelevant" on Tuesday evening, does not do nearly enough. But McConnell accused Democrats of not stepping up to the table to negotiate a "serious" proposal.

"They want to spend $3 trillion, which is double what we already added to the national debt back in March and April," he added. "That's a $2 trillion difference, it is no small amount of money."

McConnell said Democrats are also reluctant to agree to liability protections which would guard businesses, hospitals, doctors, universities, and teachers from "an epidemic of lawsuits on the heels of the pandemic."

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"All the finger-pointing is not going to get to an outcome," he said. "We need to sit down and see what we can agree to and do that and I do think with unemployment expiring at the end of the week, there is incentive for both sides to come together behind something, either a smaller package, as the president suggested was a possibility, or to get serious about doing something more significant.

"The public is interested in a result here and the only way to get a result is a bipartisan agreement."

Fox News' Tyler Olsen and Morgan Phillips contributed to this report.