Two tea party superstars – Senators Rubio and Lee, both of whom knocked out establishment Republican figures to win their seats – are going to be key players in any reform.
In the House, the involvement of House Judiciary chairman Rep. Bob Goodlatte (R) of Virginia and Representative Labrador of Idaho can provide cover to conservative lawmakers from the party's right flank.
"The fact that you're going to have strong conservative voices helping lead this debate is going to be critical to solving it instead of using it as a political wedge," says Rep. Steve Scalise (R) of Louisiana, incoming chairman of the Republican Study Committee, the largest and most conservative caucus in the House.
It's notable that both Labrador and Rubio believe in, one way or another, a path to citizenship for some illegal immigrants, even while they leave open just who can get on that path.
Some conservatives say any form of citizenship given to illegal immigrants – no matter the conditions attached to it – constitutes an "amnesty," which is a guarantee only of more illegal immigration unless the nation's borders are firmly secured and stringent workplace verification systems are put in place.
But a recent poll by George Washington University and Politico found 62 percent of Americans support a proposal that would allow illegal immigrants to earn citizenship over a period of several years, with 40 percent strongly supporting such a measure. Only 35 percent opposed it.