Immigration advocates reacted angrily Wednesday to President Obama’s declaration that he does not have the authority to completely halt the deportations of millions of people who are living in the country illegally. The heated response, from some of the administration’s closest allies, reflects the mounting frustration many feel about the diminishing prospects for immigration reform on Capitol Hill.

The blowback was further evidence of the high stakes involved for the president on one of his second-term priorities as House Republicans continue to delay action on a proposed overhaul of the nation’s border control laws.

After focusing for months on GOP lawmakers, advocates erupted at Obama after he said in a television interview Tuesday that he is powerless to scale back mass deportations — estimated at more than 1,000 per day.

“Unless the president alters course, he risks cementing his legacy as having presided over the most anti-immigrant administration in history,” said Pablo Alvarado, executive director of the National Day Laborer Organizing Network. Alvarado said Obama has an “obligation to lead the national debate through bold action

To highlight their concern, seven undocumented workers affiliated with Alvarado’s organization handcuffed themselves to the north gates of the White House on Wednesday morning, unfurling a sign with Obama’s image and the words, “Mr. President Stop Deportations.” They chanted, “Not one more!” and “Si, se puede,” a Spanish phrase that translates to, “Yes, we can,” Obama’s 2008 campaign slogan. The protesters were arrested and fined for not obeying a lawful order.

Immigration groups have long called on the administration to stop arresting and deporting unauthorized immigrants who have not committed other crimes. The administration deported nearly 410,000 people last year, a record.

During his reelection campaign, Obama announced that the administration would begin to defer deportations of young people brought to the country illegally as children — estimated at 1.7 million of the nation’s 11 million undocumented immigrants.

But Obama told Telemundo, a Spanish-language network, that expanding that program to cover more people is “not an option.” Doing so, he said, “would be ignoring the law in a way that would be very difficult to defend legally.”

Administration officials said they are employing the concept of “prosecutorial discretion,” which means focusing the limited resources of border control agencies on high-risk immigrants who have committed multiple crimes. Greatly expanding the number of deferments would undermine that legal rationale, the officials said.

Advocates scoffed at the reasoning, saying the president has far more leeway because most undocumented immigrants have not violated other laws.

“He does have the power to stop deportations, and we will keep challenging him,” said Cristina Jimenez, managing director of United We Dream, an advocacy group.

She noted that Obama had previously said he could not unilaterally halt deportations for the younger immigrants before he reversed course and did just that during his reelection campaign last year.

Advocates “will not let President Obama off the hook for his role in the moral crisis our nation faces,” Jimenez said.

The frustration has mounted as House Republicans have declined to vote on a Senate-approved immigration plan that features a 13-year path to citizenship for most of the undocumented population.

White House press secretary Jay Carney challenged House Speaker John A. Boehner (R-Ohio) on Wednesday to bring the bill to the floor and made an oblique allusion to the GOP’s low level of support among Hispanic voters.

“The House ought to do it right away and address some of the political challenges they’ve been encountering lately,” Carney said.

But the White House allies said the president cannot simply accuse Congress of not acting and hope that Republicans assume all of the public blame.

Ana Avendaño, director of immigration at the AFL-CIO, said: “No one is saying the president can solve this for the long term. Absolutely we need a clear legislative fix, no doubt. What we’re saying is that there’s a real crisis happening right now in communities across the nation, and the president has the power to relieve the pain and suffering.”

Frank Sharry, executive director of America’s Voice, which advocates for immigration reform, said that Obama is keeping pressure on Congress by saying he will continue to enforce immigration laws until a deal is reached.

But he suggested that the president’s calculus could change if lawmakers have not acted by the end of the year.

“It’s about his legacy,” Sharry said. “Does he really want to go down as the president who didn’t pass immigration reform and deported more people than any other president? That’s what motivates him.”