"Yet, amazingly, welfare — the largest budget item — has been largely exempt from discussions of fiscal reform," he added.

Sessions said welfare reform alone could get the U.S. about one-quarter of the way toward the $4 trillion in deficit reduction that many have used as a target for budget savings over the next decade. He suggested a modest decline in the rate of growth for welfare programs, and tougher standards and work requirements for these programs.

But he also suggested tying welfare reforms to immigration reform. Sessions has said the Obama administration has failed to adhere to U.S. law, which says people cannot enter the country if they are likely to become public charges.

He has pointedly called on the Department of Agriculture to curtail what he said are attempts to lure Mexican citizens to the United States with the promise that they could benefit from the Supplemental Nutrition Assistance Program (SNAP).

"One of the bedrock legal principles of immigration is that those coming to America should not be reliant on federal assistance," he said Tuesday. "That principle has been steadily eroded."

Sessions's proposal to include welfare reform constitute his first comments about the fiscal cliff of automatic spending cuts and tax increases since the November election, and is likely to be one of many statements on the subject.

So far, members of both parties have indicated support for sparing the Defense Department of some of the planned cuts, as well as maintaining current tax rates for the middle class. But it is so far unclear whether the parties will be able to agree on a plan for shifting some of these cuts to other areas.