A Nebraska senator has written a bill that would deny Social Security numbers to undocumented immigrants approved for President Obama’s new deportation amnesty, as a new congressional study finds that those granted work permits under the amnesty would be eligible for all Social Security benefits. Mr. Obama’s policy, announced Nov. 20, would grant “lawful presence” status to illegal immigrants for three years, and would grant them work permits enabling them to get Social Security numbers and driver’s licenses. The Congressional Research Service, in a memo to the Senate Judiciary Committee, said that means they are able to collect Social Security benefits, and will get credit for all of their work in the U.S., even time they were working illegally. “If the individual had work authorization at some point, all of his or her Social Security-covered earnings count toward insured status,” the CRS said in its memo. The research agency said it may be difficult for illegal immigrants to prove previous work done while in the country illegally, so maximizing those benefits could be difficult. Mr. Obama’s November policy could apply to as many as 4 million illegal immigrant parents, though analysts predict only about half that many will actually sign up. Sen. Ben Sasse, Nebraska Republican, has written a bill that would prohibit them from getting Social Security numbers. Earlier this week he and Sen. Jeff Sessions, Alabama Republican, wrote a letter to the Social Security Administration asking how many numbers have been doled out under a prior amnesty, Mr. Obama’s 2012 policy for so-called Dreamers, that granted legal status and work permits to young adult illegal immigrants who came to the U.S. as children.