Migrants recently deported from the United States sit at Centro de Recursos para Migrantes (Migrant Resource Center) near Douglas, Arizona, on Feb. 28, 2013, in Agua Prieta, Sonora, Mexico. (Jahi Chikwendiu/The Washington Post)

New momentum in Congress for a broad overhaul of border-control laws has prompted White House allies to demand that President Obama halt deportations of millions of illegal immigrants, many of whom would be allowed to remain in the country under a legislative deal.

The advocates, including the AFL-CIO and pro-immigration groups, argue that Obama should use his executive authority to expand a 2012 decision that halted deportations of young people brought to the United States illegally by their parents. The administration’s aggressive approach to enforcement — which has resulted in nearly 2 million deportations during Obama’s tenure — makes little sense at a time when Congress could be on the verge of providing legal relief, advocates say.

The push places the White House in a difficult political position as it attempts to negotiate with a House Republican caucus sharply divided on immigration. Leading conservatives said over the weekend that the chief impediment to a deal is their distrust that Obama would enforce new border-security provisions if a large portion of the nation’s 11.7 million illegal immigrants are granted legal status.

The White House has consistently said that Obama cannot legally expand the effort — known as the deferred action program — and some advisers fear that doing so would expose the president to more Republican criticism. Obama’s predicament was reflected in a muddled answer that he gave Friday during an online chat, when he was asked whether he would consider using his executive power to stop deportations.

“If, for some reason, we’re seeing it not getting done,” the president said of a legislative bill, “I will look at all options to make sure we have a rational, smart system of immigration. But I’m going to do everything I can in the coming months to see if we can get it over the finish line.”

Administration officials said Obama was not shifting his position and that he stands by previous statements that he must enforce the law. This spring, the Obama administration will surpass 2 million deportations — more than the George W. Bush administration removed from the country in eight years, in part because Congress boosted border control resources in the mid-2000s.

But immigration advocates argued that the pending legislation in Congress lends new urgency to the matter.

In a 41-page rulemaking petition to be filed Tuesday with the Department of Homeland Security, the National Day Laborer Organizing Network says that “it is sound policy and consistent with the President’s authority to make a categorical determination to prioritize resources away from the estimated 8 million” people who would qualify for legal status, and possibly citizenship, under a plan approved by the Senate last summer.

AFL-CIO President Richard L. Trumka said in an interview last week that the White House would actually improve its bargaining position with House Republicans if Obama unilaterally suspended deportations. Millions of undocumented immigrants would be allowed to join the public debate, Trumka said, putting more pressure on a party struggling to broaden its appeal with Latinos and Asian Americans.

“If I were president, I would have said the following: ‘It’s a broken system. Except for violent criminals, no more deportations until you help me fix a broken system,’ ” Trumka said.

Legal analysts said the truth probably lies somewhere between the White House’s position and the advocates’ demands. Courts have ruled that the executive branch can employ “prosecutorial discretion” in deciding which cases to enforce in light of limited financial resources.

In 2011, John T. Morton, then the director of Immigration and Customs Enforcement, wrote in a memo to his staff that the agency should make deporting violent criminals and those who could present national security risks a higher priority than minors, the elderly, people who are ill or pregnant, and those who have served in the U.S. military.

Critics say Morton’s guidelines have been haphazardly followed by agents who have sought to deport people arrested on unrelated matters through trumped-up charges.

Under mounting pressure during the 2012 election, Obama announced the deferred action program for hundreds of thousands of young people who were brought into the country illegally by their parents. Known as “Dreamers,” they are allowed to live and work in the country legally under a two-year waiver that can be renewed.

The administration points to a 10 percent drop in deportations, from 410,000 in 2012 to 369,000 last year, as evidence that it has successfully used discretion and focused on high-priority cases. More than 60 percent of those deported had been convicted of another crime, officials said.

Still, deferred action “is not a permanent solution,” said Peter Boogaard, a Department of Homeland Security spokesman. “Only Congress can comprehensively reform the immigration system.”

Republicans, and some ICE officers, have challenged the legality of the deferred action program, and a report by the Congressional Research Service last year found that the White House’s authority to defer deportations is limited.

Congress “would appear to have considerable latitude in establishing statutory guidelines for immigration officials to follow,” the report concluded, such as “prohibiting DHS from considering certain factors in setting enforcement priorities.”

But Hiroshi Motomura, a UCLA professor who has written extensively on prosecutorial discretion, said the Obama administration could, in effect, seek to formalize the Morton memos by creating a “sliding scale” of enforcement priorities.

“There’s not a clear answer how far they could go legally,” Motomura said. “But they’d hit the political limits before reaching their legal limits. No one thinks they can just suspend immigration laws. But we’re way, way short of that.”

David A. Martin, who served as principal deputy general counsel for the Department of Homeland Security in the first two years of the administration, said the amount of flexibility Obama has would probably not satisfy most advocates.

“One of the anti-deportation efforts is called, ‘Not one more,’ but it’s politically counterproductive; it’s not feasible,” said Martin, now a professor at the University of Virginia. “Not every deportation is unfeasible. Not every deportation breaks up a family.”

The “not one more” campaign was started by the National Day Laborer Organizing Network, whose tactics have included immigrants handcuffing themselves to the White House gates and blocking deportation buses in Arizona. Jessica Karp, an attorney for the group, said the rulemaking petition to the Homeland Security agency is meant to provide legal arguments to buttress the group’s demonstrations.

“The president’s stated policy since taking office is ‘enforcement on steroids’ in order to gain credibility and give him leverage on negotiations over immigration reform,” Karp said. “That strategy is a failure. It’s failed politically and caused untold suffering in the immigrant community. It’s time for a new strategy.”