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The supporters of the 2007 effort concluded that Americans didn’t trust the government to secure the borders and enforce the laws, even as they were offering legalization, particularly since illegal immigration has only grown since a 1986 amnesty.

To combat that impression, Mr. Graham and Mr. Schumer said they’ll include new enforcement at both the border and in the country’s interior.

“Once it is clear that in 20 years our nation will not again confront the specter of another 11 million people coming here illegally, Americans will embrace more welcoming immigration policies,” they wrote.

They have been working on the proposal for months, sorting out competing interests from business groups, labor unions and immigration advocates. They said their plan has four key components: a path to citizenship for illegal immigrants, a program to let in future workers, the improvements in enforcement and the biometric Social Security cards to help employers weed out illegal workers.

The senators said their legalization would be a “tough but fair” program that would require illegal immigrants to admit they broke the law and make them perform community service and pay a fine.

Illegal immigrants would also have to demonstrate they are proficient at English and pass background checks to gain citizenship.

The plan would offer permanent legal status to foreign students who earn a post-graduate degree from an American university, and creates a future program for low-skilled workers. Businesses could only hire them if no American worker is available, and the number allowed would fluctuate depending on the U.S. economy’s needs. Workers who have kept jobs for a long time and have proved valuable members of their community could earn permanent legal status.