The answer from a small but growing number of House Republicans is "yes," just as long as it's not the "special" path advocated by Democrats and passed by the Senate.
"There should be a pathway to citizenship not a special pathway and not no pathway," Republican Rep. Jason Chaffetz told ABC 4 Utah after speaking at a recent town hall meeting in his Utah district.
"But there has to be a legal, lawful way to go through this process that works, and right now it doesn't."
It's far from clear, however, what a path to citizenship that's not a special path to citizenship might look like, or how many people it might help.
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The phrase means different things to different people, and a large number of House Republicans oppose any approach that results in citizenship for people who are now in the country illegally.
Nonetheless, advocates searching for a way ahead on one of President Barack Obama's second-term priorities see in the "no special path to citizenship" formulation the potential for compromise.
"I think there's a lot of space there," said Clarissa Martinez, director of civic engagement and immigration at the National Council of La Raza, a Latino advocacy group. "And that's why I'm optimistic that once they start grappling more with details, that's when things start getting more real."
House Republicans have rejected the Senate approach, promising to proceed instead with narrowly focused bills, starting with border security. No action is expected on the House floor until late fall, at earliest, because of pressing fiscal deadlines that must be dealt with first.