WASHINGTON (AP) — A surging Rick Santorum is running even with Mitt Romney atop the Republican presidential field, but neither candidate is faring well against President Barack Obama eight months before Americans vote, a new survey shows.

Obama tops 50 percent support when matched against each of the four GOP candidates and holds a significant lead over each of them, according to the Associated Press-GfK poll. Republicans, meanwhile, are divided on whether they’d rather see Romney or Santorum capture the nomination, with Newt Gingrich and Ron Paul lagging behind. It’s a troubling sign for the better-funded Romney as the GOP race heads toward crucial votes in his home state of Michigan, in Arizona and in an array of states on Super Tuesday, March 6.

“I’d pick Santorum, because it seems Romney may be waffling on a few issues and I’m not sure I trust him,” said Thomas Stehlin, 66, of St. Clair Shores, Mich. He thinks the Detroit-born son of a Michigan governor is facing a strong challenge from Santorum in his home state because of his tangled answers on the auto industry bailout.

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Also, he says, there’s this: Romney, the self-described can-do turnaround artist of the corporate world and the troubled Salt Lake City Olympics, with his millions of dollars, has been unable to vanquish his political opponents.

“That may be the reason right there,” said Stehlin, a retired government worker and a Republican. “He spends lots of money and he doesn’t get anywhere.”

Nationally, Republicans are evenly split between Romney and Santorum. The poll found 33 percent would most like to see Santorum get the nomination, while 32 percent prefer Romney. Gingrich and Paul each had 15 percent support.

Romney’s fall from presumed front-runner to struggling establishment favorite has given his opponents an opening as he tries to expand his support. His Republican rivals have stepped in claiming to be a more consistent conservative and viable opponent against Obama, and each of the last three AP-GfK polls has found a different contender battling Romney for the top spot. But Santorum, the former Pennsylvania senator and abortion foe, has hit his stride at a key moment in the nomination contest.

Santorum’s spike comes as satisfaction with the field of candidates remains tepid and interest in the contest is cools. About 6 in 10 Republicans in the poll say they are satisfied with the people running for the nomination, stagnant since December and below the 66 percent that felt that way in October. Only 23 percent are strongly satisfied with the field and 4 in 10 said they are dissatisfied with the candidates running, the poll found. And deep interest in the race is slipping: Just 40 percent of Republicans say they have a great deal of interest in following the contest, compared with 48 percent in December.

“It seems like in the last month or so everything’s just chilled out,” said James Jackson of Fort Worth, Texas, a 40-year-old independent who leans Republican. “I just haven’t been following it lately.”

Santorum remains Romney’s biggest threat. He won GOP contests in Iowa, Minnesota, Missouri and Colorado, stunning the GOP establishment that Romney has methodically courted since his first bid for the GOP nomination in 2008. The poll suggested more people are getting to know and like Santorum, with 44 percent of all adults saying they have a favorable impression of him, compared with 25 percent in December. The share with negative views has grown as well, with 42 percent having an unfavorable opinion of Santorum.

Among Republicans in that time period, Santorum has shot from 37 percent to 70 percent favorable.

There’s evidence that Santorum’s comments about social issues may not have hurt him so far among women.

The former Pennsylvania senator has been unapologetic in his opposition to abortion and his concerns about working moms, women in combat and contraception — some of the many examples he cites while making the case that he would draw a clearer contrast than Romney against Obama.

For all that, there’s little evident gender gap between Romney and Santorum, the AP-GfK poll showed. Santorum, who made some of the comments while the poll was being conducted Feb. 16-20, runs even with Romney among both Republican men and women. And Republican women may be rallying to his defense: Seventy-five percent of GOP women have a favorable impression of Santorum, compared with 66 percent of Republican men, the poll found.

The enduring split between Romney and whichever Republican opponent is up at any moment reflects a familiar dispute in the broader GOP over whether to focus on social issues or financial matters in presidential races. According to exit and entrance polls conducted so far this cycle, Romney has carried voters who called the economy their top issue in 4 out of 5 states, while Santorum has drawn broader support among those calling abortion their top concern. Abortion has lagged well behind the economy as a priority for voters through the Nevada caucuses, but the recent focus on social issues in the campaign could increase its importance.

Among conservative Republicans, Santorum holds a decisive edge, with 41 percent preferring him and 27 percent supporting Romney. But ask moderate and liberal Republicans the same question and the results flip: Forty percent favor Romney while 20 percent prefer Santorum.

Similarly, tea party Republicans also favor Santorum over Romney, 44 percent to 23 percent. Non-tea partyers tilt toward Romney, with 38 percent preferring him and 25 percent supporting Santorum.

Santorum enjoys an edge among Republicans age 45 and up, those paying the closest attention to the GOP race and born-again and evangelical voters.

Looking ahead to the general election, Obama holds an 8-point lead over Romney, 9 points over Santorum and 10 points over Gingrich or Paul, the survey found.

Notably, the survey showed the president dominating among independents, a group central to Obama’s 2008 victory, whose support for him had faltered in recent months. According to the poll, 6 in 10 independents would choose Obama over any of the Republicans.

There was good news for Republicans, too: Any of the four Republican candidates would likely top Obama among those age 65 and over, as well as among whites without college degrees.

For their part, Democrats were watching with some glee.

“It’s been a great show,” said Karen Clark, 38, a radio personality from Raleigh, N.C., who’s voting for Obama.

The Associated Press-GfK Poll was conducted Feb. 16-20 by GfK Roper Public Affairs & Corporate Communications. It involved telephone interviews with 1,000 adults nationwide and has a margin of error of plus or minus 4.1 percentage points.

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Associated Press writers Dennis Junius and Stacy Anderson contributed to this report.

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Copyright 2012 The Associated Press.