Sen. John McCainJohn Sidney McCainCindy McCain endorses Biden: He's only candidate 'who stands up for our values' Biden says Cindy McCain will endorse him Biden's six best bets in 2016 Trump states MORE (R-Ariz.) stopped short of urging Speaker John BoehnerJohn Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE (R-Ohio) to abandon his pledge to require majority support from the GOP conference before bringing an immigration bill to the House floor.

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Asked whether he believes BoehnerJohn Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE should break the Hastert Rule to push immigration reform, McCain demurred.

"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."