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Mr. Wolf said that in addition to rejecting citizenship, other objectives must be met for him to vote for a bill, including control of the borders. He said voters have little faith that the Homeland Security Department can do protect the border, so he would want independent observers, such as Southwestern governors, to be part of the certification process.

All those approaches are at odds with the massive bill that the Senate passed in June on a 68-32 vote. It grants eventual citizenship rights to most illegal immigrants, requires more money to be spent on border security and rewrites the legal immigration system to let in more guest workers and employment-based immigrants.

House Republicans have declared that bill dead. Instead, GOP leaders have signaled they that they would take up pieces of the issue, including border security, interior enforcement, guest-worker programs and at least one legalization bill that would apply to so-called Dreamers, the illegal immigrants brought to the U.S. as minors by their parents and carry the most sympathy in the debate.

Activists say that if the House doesn’t pass broad legalization, Republicans will be labeled anti-immigrant and anti-Hispanic. Luis Aguilar, an activist with Casa en Action who was protesting outside Mr. Wolf’s suburban office, said citizenship is not negotiable.

“In my case, I’ve been here 15 years. There are people who’ve been here over 20 years,” said Mr. Aguilar, 25, one of those who got tentative legal status under President Obama’s non-deportation policy for young illegal immigrants. “We won’t stand for anything other than citizenship.”

The five dozen activists who marched alongside him chanted slogans mostly in Spanish, though the signs they held were mostly in English.

Wolf, escucha, estamos en la lucha,” they chanted, which translates roughly as “Wolf, listen up, we are in the struggle.”

Among the signs was one posing the political question “GOP — RIP? The choice is yours.”

“The demographics are changing in this district,” Mr. Aguilar said of Mr. Wolf’s seat, which stretches from the inner Washington suburbs to West Virginia. “He should be aware that he cannot continue with the same voting patterns.”