McConnell is pushing for Democrats to bring the debate to the floor when Congress returns in September, before the November elections.
"So we look forward to the debate over the appropriateness of raising taxes in the middle of a recession, between now and the election," he said.
House Majority Leader Steny Hoyer (D-Md.) said today he would prefer to deal with the expiring tax cuts before the elections, but acknowledged work on them could slip until afterward.
House leaders have said they plan to extend most of the tax cuts while letting those for the wealthiest Americans expire. Democratic leaders and President Obama have pushed for extending the bulk of the tax cuts, but have said they would like to see taxes spring upward for individuals making more than $200,000 per year, and households earning more than $250,000 in a year.
Senate Minority Whip Jon Kyl (R-Ariz.), who has expressed his support for continuing tax cuts for the nation's wealthiest Americans, argued today that even "most economists do not believe that you can even begin to tax your way into a balanced budget, when you increase the deficit by that much and thus increase the debt by that much."
Kyl said the economy can't recover if taxes are raised.
"That can't be done if you take that money out of the private sector, in the form of tax increases. So we should be very clear, to follow up on what Leader McConnell said, that you cannot tax your way out of this problem. You need to grow. And in order to grow, you don't raise taxes in the middle of an economic downturn."
Congress will have about four weeks to deal with the issue and several others, including passage of a continuing resolution before the Oct. 1 start of fiscal 2011.
—Michael O'Brien contributed to this story.