WASHINGTON -- Just over half of Americans say torture is at least sometimes justified to thwart terrorist attacks and are evenly divided over whether to close the Guantanamo Bay prison, according to a poll that underscores the challenges President Barack Obama faces in selling his terror-fighting policies.

Even so, the latest Associated Press-GfK survey also shows that Obama enjoys broad confidence that he can effectively handle terrorism in an era when many people say they still fear becoming a victim of it and when a swath of the public shares the views of Obama's Republican predecessor, George W. Bush.

At the same time, Obama hasn't lost support -- he has a strong 64 percent job-approval rating -- and nearly half of Americans still think the country's headed in the right direction. That's despite bipartisan rebukes of the new president's ordered closure of the Cuban island facility and former Vice President Dick Cheney's sustained criticism of Obama's approach to terrorism.

Terrorism and Guantanamo emerged in the poll as intensely partisan issues, with viewpoints largely split along ideological lines.

"To uphold the integrity of our Constitution for ourselves and for the world, it is important" that the U.S. close the Guantanamo prison, said Diana Jones, 68, a Democrat from Timonium, Md., who has faith in Obama's terror-battling abilities. "We need to treat other counties as we would want them to treat us." Plus, she added, keeping the prison open puts U.S. troops overseas at risk.

Countered Steve Marsh, 50, a Republican from Guntersville, Ala., who doesn't think Obama is strong enough on terrorism: "I'd just rather see them there than see them here on our soil. ... They don't, in my opinion, deserve to be treated as part of our prison system here. They need to be kept separate."

Such issues have dominated Obama's agenda in recent weeks as he has wrestled with the fallout of Bush-era policies and the legal questions surrounding them, while trying to fend off criticism from friends and foes alike.

Obama ordered the prison's closure and emphatically stated "we don't torture" just days after taking office as he sought to improve a sullied world image. But since then, he has found that making good on those campaign promises has, perhaps, been more difficult than anticipated.

The Democratic-controlled Senate demanded more details of Obama's plan when lawmakers voted 90-6 to refuse to give him $80 billion he requested to shutter the Bush-created prison at Guantanamo Bay, Cuba, by early 2010. Republicans also spoke out vigorously against the notion that dangerous terrorism suspects could end up confined on U.S. soil. And foreign allies balked at accepting the transfer of prisoners from the Navy-run facility when the United States didn't appear willing to do the same.

All that prompted Obama to deliver a speech in which he denounced "fear-mongering" by political opponents and insisted that U.S. maximum-security prisons can safely house the prisoners. He also argued anew that closing the prison, which has held hundreds of detainees for years without charges or trials, could make the U.S. safer because the prison would no longer motivate enemies overseas.

A novice commander in chief, Obama risks further defeat of his policies in Congress and disapproval of them abroad if he can't get the public on board. Thus, he's making a tough sell.

For now at least, the AP-GfK poll shows most Americans have faith in him, with 70 percent saying they are confident of Obama's ability to address terrorism. That's divided along party lines, with nearly all Democrats, two-thirds of independents and just over a third of Republicans expressing confidence.

Nearly eight years after terrorists struck on U.S. soil, more than a third of Americans say they worry about the chance that they or their relatives might fall victim to a terrorist attack -- essentially unchanged from 35 percent five years ago.

All that said, the poll also shows potential areas of political vulnerability for Obama and indicates he must walk a fine line as he seeks to both protect the country and turn the page on Bush's national security policies.

Some 52 percent of people say torture can be at least sometimes justified to obtain information about terrorist activities from suspects, an increase from 38 percent in 2005 when the AP last asked the question. More than two-thirds of Republicans say torture can be justified compared with just over a third of Democrats.

On Obama's plan to close the Guantanamo prison, 47 percent approve, while 47 percent disapprove. Again, the country is divided on partisan lines, with most Republicans disapproving and most Democrats approving. Independents are evenly divided.

Despite the president's safety assurances, more than half of Americans say they would be worried about the chance of terrorism suspects escaping from U.S. high-security prisons. Yet again, more Republicans express concern than Democrats. Still, the figures indicate that the GOP-fueled fear may be resonating.

Leading the charge by Republicans against Obama's policies is Cheney, who the poll shows may be benefiting from his outspokenness since leaving office. Nearly a quarter had a favorable opinion of the former vice president, a measure that's risen steadily from a low of 13 percent in one 2007 poll.

For all the out-of-power GOP's angst, the poll found one bright spot for it: More people identified themselves as Republican than did last month, 23 percent to 18 percent.

The AP-GfK Poll was conducted May 28 to June 1 by GfK Roper Public Affairs & Media. It involved landline and cell phone interviews with 1,000 adults nationwide and has a margin of sampling error of plus or minus 3.1 percentage points.