Speaker of the House John Boehner (R-OH) answers a question at a news conference on Capitol Hill in Washington. Some Republicans, including Boehner, have shifted their rhetoric on immigration since the election (Larry Downing/Reuters)

A growing number of conservatives are softening their views on immigration in the wake of President Obama’s dominating performance among Hispanic voters, giving new momentum to a years-long push by advocates to legalize millions of undocumented immigrants.

Yet even as officials in both parties pledged to make overhauling immigration a top goal in the coming months, it became clear Friday that the issue remains thorny for each side.

House Speaker John A. Boehner was criticized by some in his party for a Thursday interview in which he endorsed passing a “comprehensive” plan, adopting the language of immigrant advocates pushing for citizenship.

By the time Boehner faced reporters for a Friday news conference, his remarks were more tepid, focusing primarily on the border-security theme that is more comfortable terrain for Republicans.

“I’m not talking about a 3,000-page bill,” he said. “What I’m talking about is a common sense, step-by-step approach [that] would secure our borders, allow us to enforce the laws and fix a broken immigration system.”

Pressed on whether he would ever support giving illegal immigrants the chance to be citizens, the speaker demurred: “I’m not going to get into any of the details of how you would get there. It’s just time to get the job done.”

The issue promises to also be complicated for Obama and his fellow Democrats, who will face unprecedented pressure from a newly empowered political base to secure a complete victory, citizenship path and all.

Hispanic leaders decided to cut Obama a break and support his reelection, despite what they considered his broken 2008 campaign promise to push immigration in his first term, but now several major organizations are planning an extensive grass-roots push next year to pressure White House officials.

“They understand they can’t make that promise twice in a lifetime,” said Eliseo Medina, secretary-treasurer of the Service Employees International Union, which spent millions recruiting new Hispanic voters this year. “For the White House and the Democrats, we don’t want to hear any more, ‘We’re with you but [the Republicans] won’t let me.’ That ain’t good enough anymore.”

The Obama dilemma could come into focus early in the debate, if Republicans and some advocates seek to negotiate smaller, scaled-back ideas as a starting point.

A key demographic

The sudden burst of activity on the right and left reflects what activists describe as a sea change in the push for immigration legislation, which has been stymied since conservatives thwarted efforts by former president George W. Bush to pursue an overhaul following his 2004 reelection.

Unlike then, activists said Friday, many conservatives now see the danger of alienating Hispanic voters. And, in contrast to the Bush strategy, which focused on backroom negotiations on Capitol Hill, advocates have decided their best hope now is to apply outside pressure on skittish politicians in both parties.

Supporters of a new law were thrilled Friday with the news that two prominent conservative thinkers, talk show host Sean Hannity and columnist Charles Krauthammer, both expressed support for legalizing illegal immigrants.

Hannity used the movement’s chosen phrase, calling for a “pathway to citizenship,” saying he had “evolved” on the matter, while Krauthammer, in his Friday Post column, described the GOP’s hard-line stance on illegal immigration as the single policy shift required to bring Hispanics back to the party.

“Border fence plus amnesty. Yes, amnesty,” Krauthammer wrote, citing the word long used by conservative opponents of a path to citizenship. “Use the word. Shock and awe — full legal normalization (just short of citizenship) in return for full border enforcement.”

The post-election discussion on the right reflects a more fundamental shift that has been happening for months among several core Republican constituencies, with a growing number of evangelical leaders, business executives and law enforcement officials expressing support for legalizing immigrants. The Southern Baptist Convention voted last year to support a “just and compassionate path to legal status.”

Some of the movement has come about as part of a new campaign called “Bibles, Badges and Businesses,” orchestrated by the National Immigration Forum. The group’s executive director, Ali Noorani, said the program has targeted leaders in both parties and has set the stage for Obama and lawmakers to feel a “different kind of pressure” than they have in the past.

Grover Norquist, the anti-tax activist and a key conservative advocate for citizenship, said he is convening a strategy session this month of like-minded conservatives to begin hunting for more support on the right for a bill to be passed soon.

“If you’d asked me a month ago, I’d have said we were five years out” from immigration legislation passing, Norquist said. “Now I think we’re 18 months out.”

How will he and others convince skeptical House Republicans? “The way it happens is evangelicals will increasingly be louder, the business community will be louder, the high-tech community will be louder,” he said.

Conversation starter

Obama, at the moment, appears to be in a strong position to begin the discussion. Exit polls showed he won 71 percent of the Hispanic vote, and that Hispanics turned out in large numbers to boost his candidacy in the key states of Colorado, Nevada and Florida. About two-thirds of voters — including most independents and 51 percent of Republicans — said most illegal immigrants working in the United States should be offered a chance to apply for legal status, rather than being deported, according to the exit poll.

The president cited immigration in his victory speech early Wednesday as one of his top policy priorities. He had predicted in the final weeks of the campaign that GOP leaders would feel political pressure to compromise on the issue after the election, telling Des Moines Register editors that “a big reason I will win a second term is because the Republican nominee and the Republican Party have so alienated the fastest-growing demographic group in the country, the Latino community.”

A White House spokesman declined to comment Friday on the administration’s legislative strategy.

The biggest questions swirled around Boehner and his always unpredictable Republican caucus, which remains heavily influenced by tea-party conservatives.

A House GOP leadership aide said Friday that many rank-and-file members seemed to be “getting it,” and that Hannity’s statement was “giving cover to those who might ordinarily want to do it but wouldn’t or couldn’t.” Still, the aide said, “we’re talking about a massive piece of legislation, and those are difficult to do.”

Following Boehner’s comments Thursday to ABC News’ Diane Sawyer, in which he endorsed a “comprehensive approach,” conservative talk radio hummed with frustrated conservatives worried he was too quick to speak on the issue.

U.S. Rep. John Fleming (R-La.) issued a statement calling on Boehner to “pull back on this issue and stop negotiating in public.”

In an interview Friday, Fleming said he had heard from a number of colleagues supportive of his statement, and they planned on confronting Boehner during a caucus meeting next week.

“This hasn’t been discussed in the conference at all,” Fleming said. “The issue of immigration reform has not even been in the mix that I can recall for the last two years.”

He said the lawmakers planned to ask Boehner to “get some input” from his GOP colleagues “before negotiating in public what we will not — will not — support.”

Scott Clement contributed to this report.