Senate Republican Leader Mitch McConnellAddison (Mitch) Mitchell McConnellPortman: Republicans are 'absolutely' committed to bipartisan infrastructure bill Graham calls voting rights bill 'biggest power grab' in history The wild card that might save Democrats in the midterms MORE (Ky.) on Sunday said it was more than just the so-called "bailout fund" that's keeping him from supporting Democrats' financial regulatory reform bill.

The fund to which McConnell refers is a liquidation pool, paid into by banks, that would be used to ensure a collapsing financial firm would not damage the entire financial system.

But when asked if he would support the bill if Democrats removed that fund, McConnell told CNN's "State of the Union" he would still have other issues with the legislation, though he did not say what those qualms were.

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"What we ought to do is get back to the table and have a bipartisan bill," McConnell said. "I don't know anybody in the Senate who thinks we ought not to pass a bill, the question is what it looks like."

McConnell made headlines earlier this week when he described Democrats' liquidation fund is a back door for taxpayer bailouts. That earned him the ire of Senate Banking Chairman Chris Dodd (D-Conn.), who railed on McConnell this Thursday during a Senate floor speech.

President Barack ObamaBarack Hussein ObamaMichelle Obama shares Father's Day tribute: 'Our daughters couldn't have asked for a better role model' Biden raised key concerns with Putin, but may have overlooked others Democrats have turned solidly against gas tax MORE later slammed the Senate GOP leader during his radio address Saturday, stressing he and other GOP leaders were standing "against common sense reforms that we've proposed."

But McConnell fired back on Sunday, noting that even the president's "own Treasury secretary, who agrees with me" hopes the liquidation fund is removed from the bill.