Two members of the bipartisan Senate group that crafted a set of principles for immigration reform on Wednesday predicted Congress faces a "tough slog" to pass a bill.
"I think it could take three, four weeks," Schumer said Wednesday at an event sponsored by Politico.
"This is such an important issue to America, and it's so complicated, and it deals with every aspect, that I think we should have a full and robust debate. And by the way, the hope is that we could pass this with a nice, sizable, bipartisan majority. Because that could set the stage — make it easier for the House to pass it.
"We don't want to have just four, five Republicans," Schumer added.
McCain said "there won't be" only a small number of Senate Republicans supporting the bill.
"It's going to be a tough slog," McCain added. "It's going to be a tough, tough fight."
On Monday McCain, Schumer and six other senators unveiled their framework for passing immigration reform.
The four principles included devising a pathway to citizenship for illegal immigrants currently living in the country, increasing the number of visas for high skilled workers, setting up an employer verification system and establishing a guest-worker program.
Both Republicans and Democrats have signaled a strong interest in passing immigration reform in 2013. McCain suggested that if GOPers do not pass immigration reform it could hurt the Republican Party with Hispanic voters.
"I think the trend will continue of lack of support from Hispanic voters, and also as you look at the demographics of states like mine — that means we will go from Republican to Democrat over time," McCain said.
One sticking point that's emerged since the so-called "Group of Eight" unveiled its framework has been whether to offer the same benefits to same-sex couples who are illegal immigrants. McCain said that doing that would be a "red herring."
"I'm telling you now, if you load this up with social issues and things that are controversial, then it will endanger the issue," McCain said.
"Look, we are talking about four principles that we've got to act on … I'll be glad to talk about it and discuss what the ramifications are and all that, but if somebody views that as an important aspect of comprehensive immigration reform, then we have a fundamental disagreement."
Near the end of the discussion, McCain and Schumer circled back to support for the eventual immigration bill among House and Senate members.
"I think probably one of the scenarios is a majority of the Democrats in the House and maybe a majority of the Republicans in the House," McCain said. "I would not anticipate a unanimous Republican support, but I think there can be significant Republican support."
Schumer added that moving a big immigration bill through committee first, and then the Senate floor, would allow legislators, especially in the House, to learn about the legislation.
"Two points to make there: The larger number of Republicans we get in the Senate, the more likely, it is my judgement, that we will pass it in the House," Schumer said.
"And second, going through the process, going through committee and amendments, going through the floor and amendments, will help us hone this. The Senate is a very diverse body and we're going to get some amendments from the very conservative members and the very liberal members and it will help refine and educate House members of what this bill is about in ways that just going and talking to them couldn't."