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All sides in the debate are rushing to frame the bill on their own terms, and turning to numbers and statistics for backup.

Last week, the Center for American Progress, a left-leaning think tank that is advocating a broad legalization, said the bill would reduce illegal immigration in the future because any increase in legal immigration would be more than covered by a drop in illegal entries.

Opponents of the immigration bill disputed those numbers.

Steven A. Camarota, research director at the Center for Immigration Studies, said even assuming all illegal immigration is halted, the U.S. would have to create more than 30 million jobs in the next decade in order to make up for the past few years plus accommodate population growth and the surge of legal immigration envisioned in the bill.

He said the conclusions from the Heritage study are obvious with a look at the demographics of the population in question.

“What Heritage is showing is there’s a high cost to cheap labor,” he said. “If you really think that high school dropouts are good for the economy and good for taxpayers, we could produce them domestically. We are, actually.”

Douglas Holtz-Eakin, president of the conservative-leaning American Action Forum who joined Mr. Barbour for the conference call, said he drew a different conclusion from the study — that Social Security and other big spending programs will have to change.

“I read this in many ways as not a study that casts doubt on the value of immigration reform but as a ringing endorsement of the need for entitlement reform,” said Mr. Holtz-Eakin, a former Congressional Budget Office director who has argued for a better legal immigration system to boost the economy.

He said that Heritage made certain assumptions about illegal immigrants, including that they are likely to remain poor and have only limited economic mobility when they are legalized.

Mr. Holtz-Eakin said his experience suggests it’s difficult to capture the exact demographics and prospects of the population.