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Just after President Obama won re-election, Mr. Boehner announced that House Republicans would tackle immigration and said a “comprehensive approach is long overdue.” This week, though, Mr. Boehner stressed a piecemeal approach and drew a line in saying Congress should delay any legalization of illegal immigrants and even put off rewriting the legal immigration system until after the borders are secure.

“It’s real clear, from everything that I’ve seen and read over the last couple of weeks, that the American people expect that we’ll have strong border security in place before we begin the process of legalizing and fixing our legal immigration system,” Mr. Boehner said.

Making sure Mr. Boehner sticks to that stricter line is a key goal of rank-and-file Republicans heading into Wednesday’s meeting.

“I think we’re going to air all that out and let leadership know that the House does not act until we know that the borders are secure. That’s really our stance,” said Rep. John Fleming, Louisiana Republican. “We want to be sure he agrees with us. That’s why we’re holding this meeting.”

Mr. Boehner has said he won’t bring a bill to the House floor unless it has the support of a majority of Republicans in the chamber, which likely dooms a path to citizenship and imperils chances for getting a final House-Senate deal.

Instead, both chambers appear to be headed for a similar situation to 2006, when the Senate last passed a broad immigration bill and the House passed an enforcement-only bill, and they couldn’t come to an agreement on a compromise.

Rep. James Lankford, Oklahoma Republican and chairman of the House Republican Policy Committee, said for Senate Democrats to reject any security efforts unless they are attached to legalization and citizenship rights is a mistake.

“There are a lot of issues that we can find agreement on — let’s find the areas we can agree on, settle those, and move on and if we have some issues we can’t settle, let’s put those off for another year,” he said. “But if we find issues that we can resolve, let’s resolve those.”