McCain's tweet on Monday follows Sen. Jeff Flake (R-AZ) also saying that he wanted Brewer to veto the bill.
Brewer has not commented yet on whether she plans to veto the bill or not. She has until Friday to decide whether to veto the measure.
Arizona State Sen. Steve Pierce (R), who originally voted for the measure, recently changed his mind and now opposes the bill.
"I screwed up," Pierce told Capitol Media Services over the weekend. "I'm trying to make it right."