Rubio says it would be a mistake to push a large, comprehensive reform bill, which could draw reflexive opposition from conservatives who are suspicious of sprawling bills that remind them of the 2010 Affordable Care Act.

“One massive piece of legislation, bill, is probably not the right approach, but I do think we need a comprehensive package, several bills,” Rubio told The Hill. “Not 10, but maybe three or four that sequentially address these issues in a coordinated way.”

McCain is not yet sold on that approach. After all, he and the late Sen. Edward Kennedy (D-Mass.) managed to push a comprehensive reform bill through the Senate in 2006. McCain, who has a long history of working with Democrats, knows they would resist any effort to split immigration reform into several pieces.

“We’ll see. I think that’s one thing that needs to be discussed, whether it would be either/or,” McCain said when asked about whether immigration reform should be attempted all at once or done piecemeal.