The legislation the House plans to take up this week, the Nutrition Reform and Work Opportunity Act, is named after the 1996 legislation that added a work requirement to welfare eligibility.
The House bill would cut food stamps, or the Supplemental Nutrition Assistance Program known as SNAP, by $40 billion over the next decade and would toughen eligibility requirements.
The bill is unlikely to draw Democratic support, but Republicans like it because it would help curb dramatic increase in food stamp use, which is up by more than 70 percent since 2008.
Total spending on SNAP has increased from $35 billion in 2007 to $80 billion in 2012, according to the non-partisan Congressional Budget Office.
The House will also take up the National Strategic and Critical Minerals Production Act, which would loosen federal restraints on mining for rare earth minerals by streamlining a permit review process that now takes "over a decade" to oen that's done in just 30 days, according to the House Resources panel.
The House will also vote on the Southeast Arizona Land Exchange and Conservation Act of 2013, which would allow the development of a copper mine about 65 miles southeast of Phoenix.
According to Arizona Gov. Jan Brewer, a Republican, developing the mine would create 3,700 jobs and generate $16 billion in revenue.
Opponents say the mine, owned by a foreign entity, would damage the Tonto National Forest which was set aside for protection from development in 1955.
"These bills will foster economic growth and create jobs for the middle class," House Majority Leader Eric Cantor, R-Va.
Beyond the House floor, all eyes will be on Republicans, who control the chamber and have to come up with a spending plan that can pass both the Republican House and the Democratically held Senate.
Republicans will likely have to pass a stopgap spending measure, known as a continuing resolution, or CR, without any help from Democrats, who believe the GOP budget numbers, which include sequester cuts, don't provide adequate funding.
President Obama said on ABC's "This Week" Sunday that he wants to negotiate with Republicans on restoring money cut by the sequester by incorporating Democratic proposals that include new taxes on oil companies and companies that ship jobs overseas.
"There are ways of doing this. It's just that they haven't been willing to negotiate in a serious way on that," Obama said.
Democrats are also likely to balk at GOP efforts to tie the government spending bill to a delay or defunding of the national health care law known as Obamacare.
Republicans are debating a number of proposals that would link the spending plan needed to keep the government open and Obamacare, which is now being implemented in a way that creates enough leverage that the Democratically led Senate would be forced to support it.
One proposal by the GOP's more conservative House faction would defund Obamacare for one year and use the savings to replace the budget cuts called for under the sequester.
Off the floor, Republicans will pick up with their investigation into the Sept. 11, 2012 attack on the U.S. mission in Benghazi, Libya, which killed four Americans including Ambassador Chris Stevens.
The House Oversight and Government Reform Committee will hold a hearing on Thursday that will review the findings of a special committee appointed to review the State Department's handling of diplomatic security before the attack, as well as its response during and after the attack.