Democrats say they haven’t given up hope of acting on an immigration bill this year, despite House Speaker John A. Boehner’s comments earlier in the week essentially putting the issue out of reach.

Immigrant-rights groups and their Democratic allies in Congress said Thursday the GOP will either have to bend and pass a bill or else face political punishment at the ballot box for having stymied a key goal of Hispanic voters.

“I haven’t given up on this year yet, on immigration reform,” said House Minority Leader Nancy Pelosi, California Democrat. “I think it’s outrageous that the speaker would say that we’re not going to pass anything.”

Mr. Boehner on Wednesday said he wouldn’t be pressured into speeding a bill through the House on Democrats’ timetable, and also said he would never go into negotiations with the Senate on that chamber’s broad bill that includes legalization of illegal immigrants. That essentially dooms chances for a bill, since President Obama and Senate Majority Leader Harry Reid, Nevada Democrat, have said a full pathway to citizenship for most illegal immigrants is a bottom-line requirement for any bill.

On Thursday, Mr. Boehner underscored the stalemate, leaving immigration off his list of action for the rest of this year.

If immigration is stalled, it will only heighten the fight back in the states and over Mr. Obama’s deportation policies.

Twenty-two immigrant-rights advocates were arrested for civil disobedience in New Orleans on Thursday for blocking a federal immigration office. The advocates were protesting the Criminal Alien Removal Initiative, a new program that immigration authorities are pursuing in New Orleans.

“With comprehensive immigration reform stalled, the question is what life will be like now for the 11 million undocumented immigrants in America,” said Saket Soni, a community leader who was arrested in the protest. “We believe CARI is the answer: brutal community raids based solely on racial profiling. The CARI program, piloted right here in New Orleans, needs to be stopped before it’s expanded and replicated around the country.”

Many analysts argue that if immigration legislation isn’t done by the end of this year it won’t be taken up until after the 2014 elections, since it may be too toxic for consideration in an election year.

But Sen. Charles E. Schumer said political pressure could change that.

“I still think it’s possible this year,” the New York Democrat said at the Washington Ideas Forum hosted by The Atlantic. “But if it’s not, I think we have a real good chance to do it in the first half of next year if I had to bet money, we’re going to have an immigration reform bill on the president’s desk.”

Mr. Schumer was chief author of the Senate immigration bill, which legalizes most illegal immigrants, calls for billions of dollars to hire more Border Patrol agents and build more fencing, and rewrites the legal immigration system.

House Republicans have been working on a series of smaller bills that would boost border security and interior enforcement, rewrite guest-worker programs and legalize illegal immigrants brought to the U.S. as children.

Some Republicans have said the rocky rollout of Mr. Obama’s health law has underscored why they are reluctant to approve a 1,000-page bill tackling all aspects of immigration at once.

At a news conference Thursday, Mr. Obama acknowledged that the problems with the health law have hurt his ability to sell his agenda, but he said that shouldn’t affect immigration and called GOP arguments an excuse for inaction.

“When you’ve got a law that makes sense, you shouldn’t be looking for an excuse not to do it. And I’m going to keep on pushing to make sure it gets done,” he said.

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