Boehner earlier this month, however, vowed to not move forward with legislation unless a majority of House Republicans supported the measure.

McCain though expressed optimism that the House would pass an immigration overhaul, citing the electoral implications of failure for the GOP.

“I really don’t feel it’s appropriate for me to tell him exactly how he should handle this,” he said. “But I think Republicans realize the implications for the future of the Republican Party in America if we don’t get this issue behind us.”