"He's the president," McConnell continued. "He needs to lead. He needs to show that he recognizes the problem. He needs to do something about it."

Senate Majority Leader Harry ReidHarry ReidThe Memo: Trump pulls off a stone-cold stunner The Memo: Ending DACA a risky move for Trump Manchin pressed from both sides in reelection fight MORE (D-Nev.) followed McConnell on the floor, and rejected the idea that Obama is not involved.

"No one can suggest in any way the president's not engaged in what's going on in the country," Reid said. "He is briefed at least once a day by the vice president as to these negotiations, and following that, on most every day he meets with his advisers as to what should be the next step. So I think it's unfair to say things like 'where is the president?' "

McConnell also indicated his unease with the direction of the talks in the last few days, citing press reports that suggest the talks are working toward a more traditional deal in which Republicans get debt reduction and Democrats get a tax increase. McConnell said this would be a bad outcome that downplays the seriousness of the need to reduce the debt and keep taxes low to help the economy.

"The suggestion is this is some quid pro quo exercise between the parties," he said. "This is a dangerous trend and it is wrong, and I think it's important that we dispel it."

McConnell bristled especially at the thought of a tax increase, and said it is "mystifying" that anyone would propose a tax hike. "Not because of Republican opposition, but because of Republican and Democratic opposition," he said.

McConnell pointed out that even when Democrats ran the House, Senate and White House last year, they could not pass a tax hike. "Either someone on the other side has forgotten that there's strong bipartisan opposition in Congress to raising taxes, or someone involved is acting in bad faith," McConnell warned.

Reid's response dealt mostly with his ongoing frustration with the Senate's inability to pass legislation that Reid and other Democrats believe would help job creation. Reid had harsh words for the House, which he said is ignoring jobs bills in favor of cutting programs.

"The House of Representatives, all they do is flex their muscles on things that they want to eliminate, but the one thing they don't talk about is creating jobs," he said. "Not a word."

McConnell's remarks Thursday followed Wednesday comments from Sen. Bob CorkerRobert (Bob) Phillips CorkerOvernight Defense: Senate passes 0B defense bill | 3,000 US troops heading to Afghanistan | Two more Navy officials fired over ship collisions Senate passes 0B defense bill Corker pressed as reelection challenges mount MORE (R-Tenn.), who said he isn't sure the debt ceiling talks led by Vice President Joe BidenJoseph (Joe) Robinette BidenBiden slams Trump over golf gif hitting Clinton Overnight Tech: Equifax hit by earlier undisclosed hack | Facebook takes heat over Russian ads | Alt-right Twitter rival may lose domain Overnight Finance: CBO to release limited analysis of ObamaCare repeal bill | DOJ investigates Equifax stock sales | House weighs tougher rules for banks dealing with North Korea MORE are leading to a result that Republicans can support. Reid spent several minutes rebutting those remarks, in particular Corker's comments that the Economic Development Revitalization Act was only taken up to fill time in the Senate.

That bill would have increased funding for the Commerce Department's Public Works and Economic Development Administration (EDA) from $300 million to $500 million, but it failed in a cloture vote earlier this week.

"They killed our fourth jobs bill this year," Reid said Thursday of the EDA bill. "It seems Republicans don't care about putting Americans back to work."

"So I take it very seriously when a Republican senator says putting thousands of people back to work is a waste of time," he added.