In a coordinated, aggressive and sharp-elbowed campaign, leaders who stood behind the White House not long ago as the president called immigration reform his top second-term priority are now attacking Obama for not doing enough on his own. Dismissing Obama’s insistence that his hands are tied by the law, advocates plan to pile on until he relents — as he did once before in the run-up to an election.

This week, the president of the National Council of La Raza, the country’s largest Latino advocacy organization and one of the White House’s most loyal allies, blasted Obama as the “deporter in chief.”

In remarks on the House floor, Rep. Luis V. Gutierrez, Obama’s fellow Illinois Democrat, pointed to portraits of Presidents Clinton, George W. Bush and Obama and compared deportations under each. “President Obama has detained more immigrants in jails, prisons and detention facilities than any other president,” Gutierrez said.

The charge is not new; Obama has long faced criticism for presiding over a record number of deportations, roughly 2 million to date. Still, the strategy sends a mixed message to a key Democratic constituency before the midterm election. Democrats hoped to see immigration advocates assail Republicans who held up the overhaul bill.

Advocates suggest their goal is to play one off the other, arguing that Republicans in Congress may feel compelled to advance legislation if they think the president is on the verge of taking unilateral action.

“Republicans can either be participants in how this country advances more sensible immigration policies or they can simply sit on the sidelines while the president does it with his ‘phone and pen.’” Gutierrez said, picking up the president’s shorthand for his promise to wield his executive power to take action without Congress.

Frank Sharry, executive director of America’s Voice, an immigration advocacy group, thinks it’s likely Obama will eventually act. “The administration is deporting people every day who the administration says should be given legal status and a path to citizenship, so the question is: If Republicans continue to stall, does the president have the authority to make things better?” Sharry said. “We think he will act even though he’s not talking like it now.”

For now, the White House is absorbing the criticism, careful not to return fire and potentially alienate Latinos voters, a constituency that cares about immigration reform and has been loyal to the president.

Obama on Thursday argued that he was not the “deporter in chief” but the “champion in chief” of the stalled comprehensive immigration reform effort.

Speaking at a White House-sponsored town hall on Latinos and healthcare, the president argued he was constrained by statute in how he treats immigrants who are in the country illegally.

“I cannot ignore those laws any more than I can ignore any of the other laws that are on the books,” he said. “That’s why it’s important to get comprehensive immigration reform done this year.”

Obama has repeated a version of the comment scores of times. But it’s little surprise the immigrant community isn’t taking it at face value. The president made very similar statements about the limits of his executive power in 2012 — before he announced his Deferred Action for Childhood Arrivals order, which allowed young immigrants brought illegally to the U.S. as children to apply for work permits and avoid being deported.

Advocates want Obama to expand that order to include other immigrants with strong ties to the U.S. and no criminal history.

That’s the sort of sweeping change the White House says is beyond its power. The legal basis for the president’s deferred-action order would erode if it were expanded, administration officials say privately. But they haven’t ruled out smaller changes.

Advocates want Obama to end the Secure Communities program, which checks the immigration status of people fingerprinted at state and local jails and, if need be, notifies immigration authorities. They want to cancel agreements that allow local law enforcement officials to coordinate with immigration agents. They want the administration’s policy on prosecutorial discretion revised so fewer immigrants with minor criminal offenses are deemed “high priority.” And they want to end Operation Streamline, which brings criminal charges against border-crossers.

The administration has defended these policies and has encouraged immigration agents to focus on deporting immigrants with criminal records before those with strong family ties who pose no threat to public safety. But vacancies at the top of both Immigration and Customs Enforcement and U.S. Customs and Border Protection have made it difficult for the administration to change the culture at those agencies.

The renewed pressure from migrant advocacy groups and labor groups, such as the AFL-CIO, may provide the president with the cover to make changes in response to growing national support.

If the president does not act, he could put his party at risk in the election. There is some evidence that deportations have eroded Obama’s standing with Latino voters in the past. In late 2011, before the president issued his deferred-action order, roughly 60% of Latinos surveyed by the Pew Hispanic Center said they disapproved of Obama’s deportation policy. Among that group just 36% approved of his job performance, compared with 46% of all Latinos at the time.

The possibility that Latinos, disappointed by the president and Congress over stalled immigration, may sit out the November elections poses a danger to Democrats.

It also threatens Obama’s legacy with immigrants such as Pilar Molina, the owner of a tortilla company in Norristown, Pa., whose husband was arrested by immigration agents in January.

“President Obama has the right to stop deportations; he just don’t want to do it,” Molina said. “When I first saw President Obama, tears came to my eyes because I said, ‘He’s the one who is going to bring us out of the shadows.’ Now when I see him, I see a future that is uncertain for myself and everyone else.”

kathleen.hennessey@latimes.com

Twitter: @khennessey

brian.bennett@latimes.com

Twitter: @ByBrianBennett