President Obama is bracing for a political and legal battle with Republicans next year over his executive actions on immigration, but as he seeks to rally support against the anticipated assault, a lingering frustration among some Latinos could mean renewed pressure on him to do even more to protect illegal immigrants.

After six years in which his administration had taken a tough line on deportations, Obama’s decision to shield up to 4 million more undocumented immigrants from being removed from the country was in part aimed at repairing damage with a key constituency whose support for the president had plummeted.

Their backing will be critical for Obama in the face of GOP efforts in the coming months to block his deferred action program by denying federal funding for it or to overturn the measure entirely through legislation. Beyond immigration, the president also has been counting on Latinos to support his new health care law.

In both cases, the administration’s strategy is to enroll as many people as possible to make it politically difficult for Republicans — and, in the case of immigration, to put pressure on Congress to find a longer-lasting legislative solution in Obama’s final two years.

But as he attempts to shift the burden back to the GOP, Obama has continued to face tough questions from Hispanic activists about why he had not done more, and done it sooner. Of particular concern to the advocates are those who were left out of the new deportation protections.

Obama’s response to these competing forces could complicate his record on what he had hoped would be a legacy issue for his presidency. Recently in Nashville, where the president was touting the benefits of immigration to local communities, he was confronted by influential Spanish-language television host Jorge Ramos of Univision.

“You destroyed many families,” Ramos said, noting his administration has deported more than 2 million people. “They called you ‘deporter-in-chief.’. . .You could have stopped the deportations.”

“No, no, no. That’s not true,” Obama protested, criticizing Ramos for wanting “simple, quick answers” to the complicated and deep-rooted problem of illegal immigration.

“It does a disservice,” the president added, “because it makes the assumption that the political process is one that can easily be moved around, depending on the will of one person, and that’s now how things work.”

There is no denying the widespread enthusiasm among immigrant communities for Obama’s executive actions, and advocates have praised him for taking action on his own to limit deportations. When combined with Obama’s similar 2012 program for younger immigrants, nearly half of the nation’s 11 million undocumented immigrants could qualify for deportation relief and gain work permits — twice the number that benefited from a 1986 law that allowed them to seek citizenship. Thousands lined up in Los Angeles over the weekend for an information session to learn whether they qualified.

Yet some advocacy groups, such as the National Day Laborer Organizing Network, vowed to maintain pressure on the president to take further actions to protect the rest. Hecklers interrupted Obama during recent immigration rallies in Las Vegas and Chicago demanding that he expand relief to more undocumented people.

In an interview with The Washington Post, Ramos called Obama’s actions “the most important immigration measures in almost 50 years.” But he said that “it’s a mixed emotion that many Latinos have. They are very grateful to this president, but they are also very pained and resentful for those millions of families that have been destroyed.”

He added that Obama’s legacy on immigration will include a “footnote” on deportations that “is measured in human lives.”

Such criticism clearly frustrates Obama and his advisers who argue that the president went to the legal limits last month when he announced that undocumented parents of U.S. citizens and legal permanent residents who have lived in the country for five years are eligible to apply for three-year deportation waivers.

Administration officials emphasized that the president accomplished this in the face of active resistance from most Republicans and after the GOP-controlled House this past summer scuttled a comprehensive immigration reform bill.

“This president moved heaven and earth to get Congress to do its job,” said Cecilia Muñoz, Obama’s domestic policy adviser. She added that the nation’s deportation policies amount to “a broken law that has terrible effects on the country. But I don’t think it’s particularly fair to place at the feet of the president Congress’s failure to do its job here.”

During an immigration rally at a Las Vegas high school, the president was interrupted several times by Jose Patiño, a 25-year-old math teacher from Phoenix. Patiño and his three siblings, who immigrated with their parents from Mexico in 1996, are recipients of the Obama administration’s 2012 deferred action program for younger immigrants. But none is a U.S. citizen, meaning their parents will not qualify under Obama’s new policies.

Patiño said in an interview that he believes Obama’s decision to leave out some groups was based on politics, and he rejects the president’s rationale that he was constrained by law.

“We had to do something to get the attention of the president and the media,” Patiño said of his outburst in Las Vegas. Others in the crowd tried to shout him down by chanting “Si, se puede!” — which roughly translates to “Yes, we can!”

Obama responded to Patiño by urging the crowd to press Congress to find a legislative solution: “Not everybody will qualify under this provision, that’s the truth. I heard you and what I’m saying is we’re still going to have to pass a bill.”

Administration officials said Obama carefully crafted his executive action to withstand the type of legal challenge filed in federal court this month by Texas and 16 other states on the grounds that the president is failing to enforce immigration laws. The administration will begin enrolling immigrants into the new deferred action program by this summer.

Last week, Obama invited two leading immigration reform advocates — Frank Sharry of America’s Voice and Lorella Praeli of United We Dream — with him aboard Air Force One to Nashville as a show of solidarity. Praeli, who was undocumented for 14 years, became a legal permanent resident two years ago and she said her mother will qualify under the new program. But, she said, the parents of about half of her organization, which represents the younger undocumented immigrants known as “dreamers,” will not.

Praeli, who also spoke with Obama in Las Vegas, said that on both occasions she “conveyed a sense of ‘we’re not done.’”

“We’re happy and proud for people who will qualify,” Praeli said. “But what happens to the people who don’t qualify. How will enforcement play out in their lives?”

Salvador Cervantes, an organizer for the Center for Community Change, asked Obama that question in the president’s town hall-style immigration event in Nashville. “Thank you for the 5 million, but what about the others?” he asked.

Obama answered by saying that his executive actions also included new guidelines in the Department of Homeland Security instructing immigration agencies to focus on deporting felons, terrorists and newly arrived illegal immigrants over those who have lived in the country for many years.

“If they’re law-abiding, if they’re working, if they’re peaceful,” Obama said, “then they’re much less likely to be deported now than they would have been in the past.”