The governor's lawyers said Monday the federal government hasn't shown it has suffered actual harm from the law and instead bases its claim on speculation.
The federal government says the state law is trumped by federal law and that it has hurt U.S. relations with Mexico. It is scheduled to take effect Thursday.
Attorneys for Brewer say Mexico's disapproval of the law doesn't make it unconstitutional.
U.S. District Judge Susan Bolton is considering requests by the Justice Department, a Phoenix police officer and civil rights groups to put the law on hold.