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On Wednesday another study entered the fray — this one published by Health Affairs, a journal that covers public health policy, and it found that immigrants paid $13.8 billion more into the Medicare Hospital Insurance Trust Fund in 2009 than they collected in benefits, while native-born Americans took out a net $30.9 billion more than they paid in.

Steven A. Camarota, research director for the Center for Immigration Studies, which wants a crackdown on immigration, said that when one cuts through all the numbers, it comes down to education levels: Only 10 percent of native-born Americans lack a high school degree and just 20 percent of legal immigrants also lack one.

But a shocking 53 percent of illegal immigrants haven’t completed high school, he said, and workers with those qualifications — whether native-born or immigrant, legal or illegal — are a net drain on the government.

Mr. Camarota said even if policymakers do follow Mr. Holtz-Eakin’s advice and change the entitlement system, they will still end up shielding the poor from the changes. And since most illegal immigrants are poor, that means legalization will only be adding a larger number of folks who cannot be touched by benefit cuts.

“You can’t grow the poor and then say what we need to do is do a whole lot less for the poor,” Mr. Camarota said. “Yeah, the system isn’t viable like this, you’re going to have to make some cuts. But you’re making it that much tougher.”