WASHINGTON — They shrug at President Barack Obama and Republican challenger Mitt Romney. They’re in no hurry to decide which one to support in the White House race. And they’ll have a big say in determining who wins the White House.

One-quarter of U.S. voters are persuadable, according to an Associated Press-GfK poll, and both Obama and Romney will spend the next four months trying to convince these fickle, hard-to-reach individuals that only he has what it takes to fix an ailing nation.

It’s a delicate task. These voters also hate pandering.

“I don’t believe in nothing they say,” said Carol Barber of Iceland, Ky., among the 27 percent of the electorate that hasn’t determined whom to back or that doesn’t have a strong preference about a candidate.

Like many uncommitted voters, the 66-year-old Barber isn’t really paying attention to politics these days. She’s largely focused on her husband, who just had a liver transplant, and the fact that she had to refinance her home to pay much of his health bill. “I just can’t concentrate on it now,” she said before adding, “If there were somebody running who knows what it’s like to struggle, that would be different.”

John Robinson, a 49-year-old general contractor from Santa Cruz, Calif., is paying a bit more attention, but is just as turned off by both candidates.

“I’m just bitter about everybody. They just keep talking and wavering,” said Robinson, a conservative who backed the GOP nominee in 2008, Arizona Sen. John McCain, but is undecided between Obama and Romney. “There’s nothing I can really say that’s appealing about either one of them.”

To be sure, many of the 1-in-4 voters who today say they are uncommitted will settle on a candidate by Election Day, Nov. 6.

Until then, Obama and Romney will spend huge amounts of time and money trying to win their votes, especially in the most competitive states that tend to swing between Republicans and Democrats each presidential election. Obama and Romney face the same hurdle, winning over wavering voters without alienating core supporters they need to canvass neighborhoods and staff telephone banks this fall to help make sure their backers actually vote.

“It presents an interesting challenge to the campaigns,” said Steve McMahon, a founding partner in Purple Strategies, a bipartisan crisis management firm. “Moving to the middle means winning these voters, but it also means creating problems with your base.”

Obama has sought to straddle both the left and the middle by announcing policies that expand access to contraception and allow immigrants brought illegally to the United States as children to be exempted from deportation and granted work permits if they applied.

Both issues are popular with his core supporters and centrist voters. The president also is promoting a list of what he says are bipartisan measures that would help homeowners, veterans, teachers and police officers, and he accuses Republicans of causing gridlock by refusing to act on them. It’s a pitch intended for independent-minded voters frustrated by inaction in Washington.

Romney has broadened his tea party-infused message from the GOP primary and softened his tone as he looks to attract voters from across the political spectrum.

He abandoned the harsh immigration rhetoric on Thursday when he pledged to address illegal immigration “in a civil but resolute manner” while outlining plans to overhaul the green card system for immigrants with families and end immigration caps for their spouses and minor children. In doing so, he risked inflaming conservatives who make up the base of the Republican Party.

Overall, the poll found that among registered voters, 47 percent said they will vote for the president and 44 percent for Romney, a difference that is not statistically significant.

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