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Senate Majority Leader Mitch McConnell, R-Ky., balked at the idea of slipping infrastructure spending into the next coronavirus relief bill in a conference call with his Republican colleagues Tuesday, Fox News has learned.

A source familiar with McConnell’s call with GOP senators confirmed that the Republican leader will not support major infrastructure spending in the next coronavirus stimulus bill.

The idea is something that President Trump has signaled he may want but that McConnell addressed head-on -- setting boundaries for what he will support in the next stimulus bill.

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The call was first reported by Axios and later confirmed by Fox News.

“We need to keep the White House in the box,” McConnell said in an effort to push back against a massive increase in federal spending, according to a source. “The Democrats and the White House both need to get the message.”

McConnell himself addressed the call on the record on “Your World with Neil Cavuto” on Tuesday.

He said he agreed with President Trump on the need for an infrastructure bill but prefers a more modest proposal that would have less impact on the national debt.

“Well, we have an equal interest in doing an infrastructure bill,” he said. “We don't have an equal interest in borrowing money for future generations to pay for it.”

The senate’s top Republican has been calling for more fiscal responsibility in recent days following a series of coronavirus relief bills totaling trillions of dollars.

Last week, McConnell suggested allowing states to declare bankruptcy -- something that they currently cannot do -- rather than send additional funds to ensure pay for essential workers on the frontlines of the virus, as well as to bolster economic recovery.

That prompted condemnations from a number of high profile Democrats, including New York Gov. Andrew Cuomo, New Jersey Gov. Phil Murphy and House Speaker Nancy Pelosi.

New York Republican Rep. Peter King blasted McConnell for the comment, as well, describing him has “the Marie Antoinette of the Senate.”

For his part, McConnell said on “Your World” that Senate Republicans remain open to the idea of sending more assistance to state and local governments -- so long as it is limited in scope to address the coronavirus.

“We’re not interested in rescuing badly run states from the mistakes they made, completely unrelated to the coronavirus,” McConnell said.

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He also said the next bill should include liability protections for employers, to spare them from lawsuits over departures from social distancing or other coronavirus guidelines as the country’s shuttered economy begins to reopen.

Pelosi has already pushed back against that idea, placing the leaders of Congress’ two chambers at odds.

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But many people around the country have been pushing to see their economies reopen -- with anti-stay-at-home protests in a number of states taking place over the past two weeks.

“We have businesses brave enough to open up again, employees brave enough to go back to work,” McConnell said. “And I'm glad to see that some of the states are beginning to move in the direction of reopening.”

Fox News’ Vandana Rambaran and Sam Dorman contributed to this report.