Sen. Sessions demands new tax revenues be marked for deficit reduction

"Our Democratic colleagues, all they want to talk about is more taxes, more taxes and more revenue," Sessions said. "They are not telling us where the money is going. They're not assuring us that the money is going to be used to pay down the debt like it's suggested. So we need to see those numbers, what they plan, before any discussion is appropriate."

Sessions said he thinks "a lot" of Republicans are fine with the idea of flattening the tax code by eliminating some deductions for the wealthy, which could generate revenue without raising marginal income tax rates. But he reiterated several times that Democrats have not made it clear that they want to use this money for deficit reduction.

"They say it's for deficit reduction, but the President's budget that he submitted to us in January would increase spending another $1.4 trillion, whereas he's proposing now, I think, $1.6 trillion in new taxes," Sessions said.

"So if taxes are just ... for more spending, I think the American people need to say, 'no, you need to bring your house under control before we send you another dime.' "

For more on Sessions' comments, click here.