"The idea of illegal immigrants receiving federal benefits like food stamps or Social Security is crazy to most Americans," Akin said. "We welcome legal immigrants who can contribute to these programs and then receive benefits for which they are legally eligible.

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"Unfortunately, the rule of law is under assault by the Obama administration, particularly when it comes to immigration. This has caused numerous states to enact their own state laws to protect their citizens and borders because the federal government has failed to act."

Akin added that federal social programs are already on unsustainable paths to meet obligations to U.S. citizens, and cited press reports saying that adding 5 million illegal couples would cost Social Security $500 billion.

His Validating Entitlement Recipients Through Indicated Federal Immigration Status (VERIFI) Act, H.R. 6000, is co-sponsored by Reps. Mo BrooksMo BrooksTrump touts endorsement of second-place finisher in Alabama primary Moore, Strange advance in Alabama GOP primary Alabama GOP Senate primary: live results MORE (R-Ala.), Paul BrounPaul BrounCalifornia lawmaker's chief of staff resigns after indictment Republican candidates run against ghost of John Boehner The Trail 2016: Let’s have another debate! MORE (R-Ga.), Trent FranksTrent FranksGOP lawmaker: 'Quit electing' Dems for national security OPINION | Senate must end the tyranny of the minority and abolish the filibuster GOP House member calls on Mueller to resign MORE (R-Ariz.), Phil GingreyPhil GingreyBeating the drum on healthcare Former GOP chairman joins K Street Former Rep. Gingrey lands on K Street MORE (R-Ga.), Gregg Harper (R-Miss.), Tim Huelskamp (R-Kan.), Walter Jones (R-N.C.), Jack Kingston (R-Ga.), David SchweikertDavid SchweikertFreedom Caucus backs three debt ceiling options Bipartisan lawmakers give blood in honor of Scalise GOP senators pleased with Ivanka Trump meeting on family leave, child tax credits MORE (R-Ariz.) and Lynn Westmoreland (R-Ga.).

Also Thursday, Rep. Michael BurgessMichael BurgessMedicaid efficiency is needed now, more than ever In the politics of healthcare reform, past is prologue New hope for ObamaCare repeal? Key GOP lawmaker working on amendment MORE (R-Texas) introduced a bill that would prohibit DHS from granting a work authorization to an alien found to have been unlawfully present in the United States. Burgess and other Republicans have criticized the administration's decision not just for what they said is selective enforcement of U.S. immigration law, but for the decision to encourage illegal immigrants under 30 to apply for work authorization in the United States.

The GOP has said that decision pits unemployed U.S. workers against illegal immigrants for jobs.

"With over 12 million Americans unemployed, President Obama showed that he is not concerned with policies that will put them back to work," Burgess said last week. "Instead, he wants to put illegal immigrants ahead of the rule of law and provide them with work permits."

While Republicans have introduced a handful of bills to counter Obama's immigration decision, GOP leaders in the House have so far been mum on whether they will schedule votes on these bills. But Republicans appear split on whether to fight the decision aggressively, or to be more wary of how the issue is playing out politically, and let GOP presidential front-runner Mitt Romney take the lead.

On Thursday, House Majority Leader Eric CantorEric CantorEx-RNC spokesman: After Trump remarks how can I tell minorities to vote GOP Kelly’s challenge? Bringing stability to Trump White House Special interests hide behind vets on Independence Day MORE (R-Va.) did not mention any bills related to immigration that the chamber would take up next week, before the July 4 break.

Earlier this week, Rep. Ben Quayle (R-Ariz.) offered a bill that would prohibit DHS from implementing the administration's policy announcement. The announcement took the form of a memo from DHS that said it would exercise discretion on how it would enforce deportation proceedings against illegal immigrants.

Schweikert, who is in a primary runoff against Quayle, introduced a separate bill prohibiting executive orders on immigration from being followed, although the Obama administration's decision did not come in the form of an executive order.