Sen. John McCainJohn Sidney McCainSenate confirms Pompeo as Trump's new secretary of State GOP moves to cut debate time for Trump nominees GOP advances proposal to change Senate rules MORE (R-Ariz.) split with colleague Sen. Marco RubioMarco Antonio RubioLobbying world Former Florida congressmen mull bipartisan gubernatorial run: report Winners and losers from Jim Bridenstine’s confirmation as NASA administrator MORE (R-Fla.) and said he sees support among House Republicans for passing a bipartisan immigration reform bill.

McCain specifically mentioned House Budget Committee Chairman Paul RyanPaul Davis RyanOusted House chaplain: Ryan told me to ‘stay out of politics’ Overnight Finance: House chairman eases demands on Dodd-Frank rollback | White House economist dismisses trade war fears | Unemployment claims at 48-year low | State AGs want new hearing on Obama financial adviser rule Conservative leader: Next House chaplain should have a family MORE (R-Wis.) and Speaker John BoehnerJohn Andrew BoehnerConservative leader: Next House chaplain should have a family House chaplain forced out by Ryan Code red for the GOP MORE (R-Ohio.).

"Paul Ryan came out just a few days ago with strong support. The Speaker ... he has not criticized the bill, let's put it that way," McCain said Thursday in a radio interview with Univision. "And so I see a lot of Republicans that realize this present situation is de facto amnesty and that we need to fix it."

The comments by McCain contrast comments by Sen. Marco Rubio (R-Fla.) who, on Tuesday, said the Senate immigration bill is unlikely to pass the House in its current form.

"It will probably have to be adjusted," Rubio said.

Rubio and McCain, along with six other Republican and Democratic senators, crafted the immigration bill and unveiled it earlier in the year.

In the same interview, McCain said the bill would probably have stronger chances if it can get 70 votes in the Senate. 

"Now, one of the things that I think is going to be important is to have over 70 votes or more in the United States Senate," McCain said. "I think that's achievable. I really do. I think it's very achievable and so that would put momentum behind the bill."