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But the Republican tried to turn the tables on Mr. McAuliffe during the debate by pointing to the Democrat’s championing the EB-5 visa program, which allows foreign investors to put up between $500,000 and $1 million in job-creating American businesses in exchange for green cards and, ultimately, U.S. citizenship. GreenTech Automotive, Inc., a car company Mr. McAuliffe helped found in 2009, has relied heavily on the program for capital.

“It’s an odd place for immigration to come in, but it’s the one that he has experience in,” Mr. Cuccinelli said.