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Up to 2 million people could get conditional legal status, according to one estimate. But the Congressional Budget Office said since many of those won’t go on to college or join the military, only 700,000 will still be in conditional status and in line for legal permanent residency by 2020.

Mr. Graham, who earlier this year had tried to strike an immigration agreement with Democrats, rebuked the majority party for trying to push the bill through now, calling it a late-session political ploy.

The bill was debated for just one hour in the House, and no amendments were allowed in either the House or the Senate — a move that Republicans said proved it was a political move rather than an honest effort to pass the bill.