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“I wouldn’t throw in the towel,” she said.

Mr. Tejada, a Democrat, noted there were about 24 anti-illegal-immigrant bills filed during last year’s assembly session, including one that would bar illegal immigrants from enrolling in public colleges and universities. The county’s legislative package supports access to in-state tuition at Virginia colleges and technical schools for undocumented students — but Sen.-elect Adam P. Ebbin, Arlington Democrat, told the board not to hold out hope.

“I wouldn’t expect anything good,” he said. “It’s a question of how much bad is brought up and what would get through the Senate.”