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The Republican leader set up a procedural vote on proceeding to the bill from Sen. David Vitter (R-La.). The legislation, which was fast-tracked to the Senate floor earlier this week, restricts federal funding for cities that don't comply with federal immigration law.

Because the Senate is scheduled to be out of session next week, the cloture vote on taking up the bill is scheduled for Oct. 20.

Republicans have been focused on the issue since the death of 32-year-old Kathryn Steinle, who was shot in San Francisco, allegedly by an illegal immigrant who had already been deported five times.