Most Americans support providing a pathway to citizenship for immigrants living illegally in the U.S., provided they meet certain requirements, a new survey shows.

In all, 62 percent of those surveyed agree with this approach, while 17 percent support allowing them to become permanent legal residents but not citizens. Nineteen percent favor a policy that would identify and deport all immigrants living illegally in the U.S.

The Public Religion Research Institute and the Brookings Institution’s survey is based on telephone interviews done last month with 1,538 randomly selected adults, who were part of a similar survey last year. The margin of error is plus or minus 3.3 percentage points. Support for a pathway to citizenship remains nearly unchanged from last year, when the same poll showed 63 percent in favor.

Last year, the Democratic-controlled Senate passed bipartisan immigration overhaul legislation that would provide a route to citizenship for immigrants without legal status in the U.S. House Republicans have rejected that legislation, saying it would reward lawbreakers with “amnesty.”

Prospects for the passage of such measure dimmed Tuesday when Dave Brat — a tea party-backed candidate — defeated House Majority Leader Eric Cantor in Virginia’s Republican primary. A little known college professor, Brat accused Cantor of supporting amnesty for immigrants living in the U.S. without papers, though Cantor has opposed the Senate’s immigration bill.