Sen. John McCainJohn McCainLawmakers wary of Trump escalation in Syria Senators urge Trump to do right thing with arms sales to Taiwan Changing America: America’s growing education divide MORE (R-Ariz.) split with colleague Sen. Marco RubioMarco RubioSenators urge Trump to do right thing with arms sales to Taiwan Why liberals should support Trump — not Obama — on Cuba policy The Memo: Trump seeks to put his stamp on nation MORE (R-Fla.) and said he sees support among House Republicans for passing a bipartisan immigration reform bill.

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McCain specifically mentioned House Budget Committee Chairman Paul RyanPaul RyanOvernight Defense: Pentagon sees signs of chemical weapons activity in Syria | House votes to reaffirm NATO defense pact | Saudis refuse to ease Qatar demands Overnight Finance: GOP divided over welfare cuts in budget | Lawmaker loses M on pharma stock he pitched | Yellen says another financial crisis unlikely in our lifetimes Overnight Healthcare: Senate delays ObamaCare vote past recess | Trump says GOP 'very close' to deal | Three more senators come out against bill MORE (R-Wis.) and Speaker John BoehnerJohn BoehnerChaffetz calls for ,500 legislator housing stipend GOP super-PAC promises big spending in 2018 Ryan reminds lawmakers to be on time for votes 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."