The Alabama lawmaker said the upper chamber "should be where these great issues of finance and debt should be the No. 1 issue before the American people. It should be voted on in the Senate regularly, debated and discussed.”

But Sessions also reserved some criticism for fellow Republicans, who he argued had been too secretive about their role in deficit and tax negotiations.

"I believe the fundamental problem the Republicans have exasperated here is allowing these negotiations to go on in secret. ... [T]he American people have no idea what’s going to be agreed to," Sessions said.

The three-term senator said that conducting the negotiations in private likely benefited the Democrats, because it allowed President Obama to shape the terms of the debate.

"It hasn’t been publicly debated ... [and] this lack of clarity I think contributed to the ability of the president to be successful in this election," Sessions said.