As the Senate prepares to begin a free-wheeling debate over immigration next week, White House officials have begun floating a possible compromise idea — a pledge to maintain legal immigration at current levels, about 1.1 million people a year, for more than a decade.

President Trump has proposed a series of measures, including restrictions on family unification, which he calls “chain migration,” and an end to the visa lottery, that critics say ultimately could cut legal immigration to America by 40% or more.