Sen. John McCainJohn McCainEx-Bush aide Nicolle Wallace to host MSNBC show Meghan McCain: Obama 'a dirty capitalist like the rest of us' Top commander: Don't bet on China reining in North Korea MORE (R-Ariz.) stopped short of urging Speaker John BoehnerJohn BoehnerLobbyists bounce back under Trump Business groups silent on Trump's Ex-Im nominee Chaffetz won't run for reelection MORE (R-Ohio) to abandon his pledge to require majority support from the GOP conference before bringing an immigration bill to the House floor.
"I really hesitate to tell Speaker Boehner how he should do this," he said on “Fox News Sunday.”
A reform package passed the Senate earlier this week on a 68-32 vote, but conservatives in the House have said they can't support the bill, because they believe it lacks adequate border security provisions and because they oppose a pathway to citizenship.
Some believe reform could pass the House with the support of more centrist Republicans and the Democrats in the lower chamber.
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."