Members of Congress have introduced about a dozen bills over the last two days to either block Syrian refugees, or impose tougher verification steps on any refugees the U.S. accepts.

The bills reflect the growing worry that Republicans in particular have over taking in up to 10,000 Syrians next year, in light of France's discovery that one of last week's attackers entered that country as a refugee.

The House is already expected to pass a bill this week modeled on Richard Hudson, R-N.Y. His bill would prohibit the resettlement of Syrians until the Department of Homeland Security, the FBI and the Director of National Intelligence can "certify … that each refugee is not a security threat."

That bill, which has 35 Republican co-sponsors, would also require enhanced background checks on each refugee.

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