“I’m opposed to granting amnesty,” said Rep. Nick Rahall, a Democrat from West Virginia, whose grandparents legally emigrated to the U.S. from Lebanon. Creating a separate way this group can gain citizenship “would siphon scarce resources away from our already-overwhelmed immigration system and would be unfair to those other immigrants, past and present, who have dutifully waited for their turn to legally enter our country,” he said.

Some House Democrats fret that any new immigration laws could repeat what they consider the mistakes of a 1986 law that legalized many illegal immigrants and included measures to stop illegal crossings.

“I want to be certain that it’s not 1986 all over again,” said Rep. Daniel Lipinski, a Democrat from Illinois, who said he’s concerned some lawmakers might be willing in future negotiations to roll back the provisions to beef up border security, which were added to the Senate bill in a bid to win GOP support. “I have concerns about if the federal government will be serious about enforcing immigration law in the future,” he said.

The exact number of resistant or fence-sitting House Democrats on immigration is hard to determine. Like many Republicans, some centrist Democrats are reluctant to stake out a firm position before the House strategy is set.