The legislation does not specify how many refugees would be settled in the United States.
The legislation restricts federal funding for cities that don't comply with federal immigration law.
He said Republicans should bring a clean debt-ceiling bill to the floor "immediately."
But it's unclear when they'll try to move legislation.
He slammed the administration for not handing over a plan to close the facility.
Sen. Claire McCaskill said a recent report about contracts is raising questions.
The Senate voted 70-27 in favor of a policy bill, defying Obama's veto threat.
Sen. David Vitter's bill will head directly to the Senate floor.
The Nevada Democrat said he would speak out until Republicans shut down the committee.
Senators would roll out their "modest measure" on Wednesday.