Chances for a broad immigration bill to pass this year took a major hit Thursday when House Speaker John A. Boehner ruled out any action until President Obama proves to Republicans’ satisfaction that he is serious about enforcing the laws and no longer will try to work around Congress.

Just a week after Mr. Boehner appeared to jump-start chances for immigration by releasing House Republican principles for a bill, his comments erased most of that momentum.

“Listen, there’s widespread doubt about whether this administration can be trusted to enforce our laws. And it’s going to be difficult to move any immigration legislation until that changes,” the Ohio Republican said at his weekly press conference.

Immigrant rights groups were stunned at the reversal and warned of drastic electoral consequences among Hispanic voters if Republicans refuse to act.

CNN released a poll Thursday that suggests voters care more about granting citizenship to illegal immigrants than they do about boosting border security.

The White House remained optimistic. Press secretary Jay Carney said congressional Republicans, who a few years ago supported mass deportations, now are talking about granting some kind of legal status for illegal immigrants.

“We’ve made enormous progress in building that consensus,” Mr. Carney said. “We continue to see positive progress, and we’re going to work with Congress to get this done.”

Mr. Boehner’s new stance is more in line with many of his fellow House Republicans, who have questioned why party leaders are pushing for action on immigration when voters generally rank it low on their list of priorities.

Republicans also argue that no matter what security measures they pass, Mr. Obama can’t be trusted to follow through on them. They bristled at Mr. Obama’s promise in his State of the Union address to circumvent Congress and take executive action when he feels lawmakers aren’t bending to his will on issues such as climate change and the minimum wage.

Adding to their concerns was a reinterpretation of refugee and asylum law by the State and Homeland Security departments.

The law bars approval for applicants who give “material support” to someone tied to terrorism. The administration said that excludes some important cases and that it will apply the law only when the material support goes beyond “limited” interactions with terrorists.

House Judiciary Committee Chairman Bob Goodlatte, Virginia Republican, said the move was “changing our immigration laws” and creating a loophole that makes it easier for enemies to enter the country.

“Yet again, this administration is abusing the powers granted it by Congress to provide relief in appropriate cases,” he said.

Republicans said Mr. Obama can prove he is serious about the laws by engaging with Congress to find areas where he can work with lawmakers, such as job training and research funding.

“The president’s asking us to move one of the biggest bills of his presidency, and yet he’s shown very little willingness to work with us on the smallest of things,” Mr. Boehner said.

Mr. Obama is trapped between both sides of the issue.

In 2012, in the middle of his re-election campaign, he announced a policymaking many young illegal immigrants, the so-called Dreamers who were brought to the U.S. as children, safe from deportation. But immigrant rights advocates now want him to extend that policy to most other illegal immigrants.

Mr. Obama said that would be stretching his powers too far.

In recent weeks, Mr. Obama has given Mr. Boehner an opportunity to craft an immigration compromise.

The president praised Mr. Boehner last week after the speaker released Republican principles, which called for giving most illegal immigrants legal status and giving the Dreamers a specific pathway to citizenship.

But matching those short principles against the 1,100-page bill that passed the Senate on a bipartisan 68-32 vote in June was bound to be difficult.

Indeed, Senate Minority Leader Mitch McConnell, a Kentucky Republican who voted against the bill, said Tuesday that he didn’t think it was possible.

With chances for reform decreasing, Mr. Obama will come under more pressure from immigrant rights groups to take unilateral action and stop all deportations.

Some groups have taken to calling him “deporter in chief” and say he has sent home a record 2 million illegal immigrants during his five years in office.

“President Obama should show Speaker Boehner that he means business by taking executive action to halt the deportation of undocumented immigrants that would qualify for citizenship under legislation that can, and should, be implemented by Congress without haste,” said Eddie Carmona, campaign manager at the Campaign for Citizenship.

Immigrant rights groups said Republicans are endangering their own political future.

“Republicans need to realize this isn’t about Obama,” said Lynn Tramonte, deputy director of America’s Voice. “It’s about them.”

She said House Republicans’ only major votes on immigration in this Congress have been on crackdowns to deny illegal immigrants taxpayer-funded benefits and try to halt Mr. Obama’s nondeportation policies.

She said those actions will be tough to sell to Hispanic voters in the midterm elections and give the party a poor start headed into the 2016 presidential campaign.

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