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Some Republicans have a problem with giving illegal immigrants a pathway to citizenship, but Mr. Rubio and his allies say the estimated 11 million illegal immigrants in the U.S. right now cannot be sent home en masse and essentially are living in the country under an amnesty because their chances of deportation are slim.

According to the draft of the bill reviewed by The Times, which was dated earlier this month, the agreement could boost legal immigration dramatically.

Polling suggests that would be controversial. Most Americans tell pollsters that they want the flow of immigration to remain the same or be curbed, while less than 20 percent say it should be increased.

The draft legislation would create a pathway to citizenship for many of those who remain in the country for at least a decade under special programs such as Temporary Protected Status. Under current law, those programs are not supposed to be pathways to permanent residency.

Under the system described in the draft, future immigrants would be awarded for educational attainment, work experience in the U.S., language skills and ties to those already in the country. It is similar to systems used by other major economies, including Australia, the United Kingdom and Canada.

Under the proposed U.S. system, those with doctoral degrees would earn 50 points toward immigration, while those who have attained only high school education would earn 15 points. Owning a home would be worth 40 points, while being proficient in English would be worth 20 points. Having critical foreign language skills, as determined by the State Department, would be worth 10 points.

Those with their own health insurance would be awarded 10 points and would earn an extra 10 points for every family member for whom they also had coverage.

The draft gives the Homeland Security Department the ability to create categories of points and to adjust the existing point system — a striking grant of power to an agency that is under fire from Congress for its interpretations of immigration law.

The 2007 immigration bill that was defeated in the Senate also included a points system. That system drew criticism from some on the left, who said it put too much value on work and education and not enough value on family ties.