(CNN)Senate Majority Leader Mitch McConnell said Monday there would likely be more money approved for state and local government relief in the next legislative package Congress passes to address the coronavirus outbreak, a shift in the messaging for the Kentucky Republican.

       McConnell last week said he wasn't sure if more money -- which is a key priority for Democrats and many Republicans -- was needed and indicated he was reluctant to provide billions to some state governments he believes have mismanaged their debt.

       "There probably will be another state and local funding bill," McConnell said in an interview with Fox News Radio on Monday. "But we need to make sure that we achieve something that will go beyond simply sending out money."

       The GOP leader also defended his remarks last week -- that caused an uproar with prominent Democrats including House Speaker Nancy Pelosi and New York Gov. Andrew Cuomo and least a few high-profile Republicans -- that laws should be changed so states can declare bankruptcy to help them shed some of their debt.

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       "I wasn't saying they had to take bankruptcy. I think it's just an option to be looked at that unfortunately states don't have that option now, cities do. I wasn't necessarily recommending it. But I was pointing out they have their own fiscal problems that predate the coronavirus and I was not interested in borrowing money from future generations to fix age old problems that states have that they created themselves wholly unrelated to this," he said.

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       McConnell also said his "red line" in negotiations for the next legislative package is ensuring "litigation protections" for employers, businesses and healthcare professionals, shielding them from lawsuits, as states reopen. "The whole country will be afraid to go back to work... if businesses are afraid they're going to be sued constantly," he said.

       "The next time we pass one of these relief bills, and we probably will, we will be more directly involved with everybody back here, able to discuss things more easily than remotely," he also said, adding, "liability protection ... is the one thing that will be part of any new bill."

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       "Before we start sending additional money down to states and localities, I want to make sure we protect the people we already sent assistance to, who are going to be set up for an avalanche of lawsuits if we don't act," McConnell said.

       McConnell's views on that issue are likely to run into opposition from many Democrats.

       Asked about reports that Democrats are feeling confident about retaking the Senate majority in 2020, McConnell said "the Senate majority has not been a certainty at any point this cycle. We always knew from the beginning and I said consistently is that it's a dogfight."

       He also added that "the other thing that's not new is that we're being outspent these days ... I think it is also true that the Democrats are doing a better job at raising funds in recent years than we have, but we took the Senate in 2014, we kept it in 2016, we increased our number in 2018, so the fact the Democrats are raising more money shouldn't raise any eyebrows, that's been the case. Now we do have a lot of exposure, this is the big class that took the majority in 2014. So we have a lot of people up."

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       It'll be a fight until the finish, he said, like "a knife fight in an alley."

       McConnell also said it was "probably a good idea" for President Donald Trump to change up the daily White House coronavirus press briefings and prioritize health professionals.

       "Certainly what the American people are most interested in is advice from health professionals on how to conduct their daily lives safely," McConnell said. "And to the extent that the White House decides to re-craft those briefings to reflect that goal, probably a good idea."

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