House Appropriations Chairman Hal Rogers (R-Ky.) postponed the release of a continuing resolution (CR) on Thursday under pressure from his party's conservative base to cut upward of $100 billion from President Obama's fiscal 2011 request, which wasn't enacted.
The stopgap measure, which expires March 4, is keeping the government running at 2010 levels.
"It's exciting if they can do it," Sessions said. "I'll look at it. But I expect I could support it."
He said he hopes the White House offers a serious plan to cut spending in its budget, arguing that President Obama hasn't shown any willingness to reduce spending and "they'll need to show that desire in a budget request."
He did acknowledge that the debt limit has to be raised "as painful as that is," he told reporters.
He also said he is "as reluctant as any Democrats to mess" with Social Security and Medicare.
"We must be very respectful," he said.
Any plan to cut that much funding by $100 billion is expected to hit a legislative brick wall in the Senate and could likely lead to a short-term extension to keep the government running until an agreement on lowering spending can be worked out.
The House is expected to release the new CR language on Friday and put the bill on the floor by Monday.
The Congressional Budget Office is estimating that the federal budget deficit will hit a record $1.5 trillion this year, fueled by an additional $400 billion from the $858 billion comprehensive legislation enacted in December that extended 2001 and 2003 tax cuts as well as federal unemployment insurance through 2011.
Meanwhile, Senate Majority Leader Harry Reid (D-Nev.) and Sen. Charles Schumer (D-N.Y.) called on Republicans on Thursday to reduce spending by cutting waste and excess, not initiatives that keep our economy growing.
They also urged House Republicans not to let their "infighting cause a government shutdown."
"One thing is abundantly clear: We have to start living within our means so we can invest in our future," Reid said. "We're eager to work with Republicans to cut spending and reduce our debt in a responsible way. The House Republicans’ proposal isn’t responsible. Instead of focusing on waste, they want to cut funding for initiatives that help us grow our economy and make our country more competitive."
Instead, Reid and Schumer urged Republicans to eliminate subsidies to big oil companies that GOP leaders say would result in a tax increase and discourage more domestic production of oil and gas.
"The question is not whether to make cuts, but what should be cut," Schumer said. "We need to invest in the programs that help us grow, and cut what doesn’t. Right now, different factions of the House Republicans keep trying to outbid each other on spending cuts," he said.
"They are blindly swinging a meat axe to the budget when they should be using a scalpel. Some of these House Republicans won’t be satisfied with anything less than a shutdown of the government."
Republicans have said they'd like to avoid a government shutdown but haven't taken the possibility off the table.
Sessions said he wasn't sure how the budget battle would pan out but reiterated his opposition to the president's proposal in his State of the Union address to freeze non-defense spending at current levels for five years because "it's inflated" and "it's really not a cut."
He did make several suggestions including reducing the corporate income tax that is "costing jobs" and making the nation uncompetitive in business.
He also advocated for a repeal of the healthcare law, increasing domestic production of oil and gas and looking at labor laws that he says are allowing too many illegal immigrants to get jobs.