"Well, I'm concerned about the task ahead of us," he said on "Fox News Sunday." "I believe that Speaker (John) Boehner has a tough job ahead. I admire his leadership. But we've got a lot of work to do."
But Sen. Chuck Schumer, another one of the bill's drafters who also appeared on the show Sunday, said he thinks that despite some objections, the House will pass the Senate's bill by the end of the year.
"We're not going to let this issue go away," Schumer said. "The strong supporters of immigration are going to be at the town hall meetings of Republican congressmen. They're going to be visiting them in their offices. They're going to be traipsing in the halls of Congress."
McCain also said that he thinks Congress will take the step and respond to the public opinion on the issue.
"When you ask the American people if they support this, if these people are here illegally paid back taxes, learn English, get in line behind everybody else," he said. "Plus, a tough border security provision, plus, an E- Verify, in other words, everybody who applies for a job better have the right documentation -- then I think you've got a winning combination here."
He also said the passing of the bill is necessary for the Republican Party's chances.
"But I think Republicans realize the implications of the future of the Republican Party in America if we don't get this issue behind us," he said.