WASHINGTON (AP) — More than 6 in 10 Americans now favor allowing illegal immigrants to eventually become U.S. citizens, a major increase in support driven by a turnaround in Republicans’ opinions after the 2012 elections.

The finding, in a new Associated Press-GfK poll, comes as the Republican Party seeks to increase its meager support among Latino voters, who turned out in large numbers to help-re-elect President Barack Obama in November.

Emboldened by the overwhelming Hispanic backing and by shifting attitudes on immigration, Obama has made overhauling laws about who can legally live in the U.S. a centerpiece of his second-term agenda. In the coming weeks, he’s expected to aggressively push for ways to create an eventual pathway to citizenship for the estimated 11 million illegal immigrants already in this country.

The poll results suggest that the public overall, not just Hispanics, will back his efforts. Sixty-two percent of Americans now favor providing a way for illegal immigrants in the U.S. to become citizens, an increase from just 50 percent in the summer of 2010, the last time the AP polled on the question.

In an even earlier poll, in 2009, some 47 percent supported a pathway to citizenship for illegal immigrants.

Further boosting the president on the issue, Democrats have opened a 41 percent to 34 percent advantage as the party more trusted to handle immigration, the first time they’ve held a significant edge on the matter in AP-GfK polling. In October 2010, Republicans held a slight edge over Democrats, 46 percent to 41 percent, on the question of who was more trusted on immigration.

Much of the increase in support for a path to eventual citizenship has come among Republicans. A majority in the GOP — 53 percent — now favor the change. That’s up a striking 22 percentage points from 2010. Seventy-two percent of Democrats and 55 percent of independents like the idea, similar to 2010.

The findings suggest that those GOP lawmakers weighing support for eventual legal status for illegal immigrants could be rewarded politically not just by Democrats and independents but also by some in their own party as well. This comes amid soul-searching in the party about how the GOP can broaden its support with Latinos, who backed Obama over Republican presidential nominee Mitt Romney, 71 percent to 27 percent, in November. Romney received less support from Latinos than Republican President George W. Bush did. But his slice was on par with candidates Bob Dole in 1996 and George H.W. Bush in 1992.

Some Republicans have concluded that backing comprehensive immigration reform with a pathway to citizenship is becoming a political necessity. Many lawmakers remain strongly opposed, and it’s far from clear whether Congress will ultimately sign off on such an approach. But in the Senate, a bipartisan group of lawmakers is working to draft immigration legislation, and Sen. Marco Rubio, R-Fla., a possible 2016 presidential candidate, has offered proposals that would ultimately allow illegal immigrants to attain legal status.

One poll participant, Nick Nanos, 66, of Bellmore, N.Y., said that providing a way for illegal immigrants to become citizens would respect America’s history as a nation built by immigrants.

“We act as if our grandparents got here legally. Don’t want to ask a single Indian about that,” Nanos said in a follow-up interview. “I don’t think that most of us can solidly come to a point where our grandparents or great-grandparents or great-great-grandparents were here legally. What does that even mean?”

Overall, 54 percent in the poll said immigration is an important issue to them personally, a figure that’s remained steady over the past couple of years.

Republicans aren’t the only group whose views have shifted significantly. In August of 2010, just 39 percent of seniors favored a path to citizenship. Now, 55 percent do. Among those without a college degree, support has increased from 45 percent to 57 percent.

And 59 percent of whites now favor a way for illegal immigrants to gain citizenship, up from 44 percent in August 2010, and 41 percent in September 2009.

Overall, the poll found 35 percent strongly favored allowing illegal immigrants to become citizens over time, while 27 percent favored the idea somewhat. Just 35 percent of Americans opposed the approach, with 23 percent strongly opposed and 12 percent somewhat opposed. That compared with 48 percent opposed in 2010 and 50 percent in 2009.

The poll also found strong support for Obama’s decision, announced last summer, to shield as many as 800,000 immigrants from deportation with conditions. Those affected would have to be younger than 30, would have to have been brought to the U.S. before turning 16 and would have to fulfill certain other conditions including graduation from high school or serving in the military. Illegal immigrants covered by the order now can apply for work permits. The order bypassed Congress, which has not passed “DREAM Act” legislation to achieve some of the same goals for younger illegal immigrants.

Sixty-three percent of Americans favor that policy, while 20 percent oppose it and 17 percent are in between or unsure, the poll said. The policy is supported by 76 percent of Democrats, significantly more than among Republicans (48 percent) or independents (59 percent).

Cordel Welch, 41, of Los Angeles, was among those poll participants who believes illegal immigrants brought to the country as children should be treated differently from people who came here as adults.

“The ones that were brought here by their parents, they’re already here, they’re already established,” Welch said in an interview. “The adults should go through the process.”

Melissa Johnson, 40, of Porter, Texas, disagreed.

“I think there were generations of people that came over here legally, and just because your parents snuck you in or snuck in while pregnant with you doesn’t give you automatic citizenship,” she said. “I think they should send them all back home.”

The Associated Press-GfK Poll was conducted Jan. 10-14, 2013, by GfK Roper Public Affairs and Corporate Communications. It involved landline and cellphone interviews with 1,004 adults nationwide. Results for the full sample have a margin of sampling error of plus or minus 4 percentage points; the margin is larger for subgroups.

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Online: http://www.ap-gfkpoll.com

Director of Polling Jennifer Agiesta contributed to this report