As House Republicans took a tentative step forward on an immigration overhaul this week and raised the possibility of citizenship for those brought to the United States illegally as young children, immigration advocates found themselves pondering a new question: Is the potential concession as far as many House Republicans are willing to go, or are they slowly inching their way toward a broader compromise? …

“The most optimistic interpretation is that leading House Republicans are testing the waters in hopes they can bring enough of their caucus along to get to a more conservative approach to a broad bill — one that would include legalization of the 11 million, with a citizenship option for many,” said Frank Sharry, the executive director of America’s Voice, a pro-immigration group. “A more cynical take is that they are trying to position themselves to win the blame game.” …

Other Democrats see the path for Dreamers as a positive step, and a signal that House Republicans might be willing to go even further in eventual negotiations with the Senate. For similar reasons, some House Republicans are hesitant to support any immigration bill, worried that it could serve as a Trojan horse that would lead to, in the words of Mr. Labrador, “having the Senate bill jammed down our throats.”