Forty-eight percent of Americans want the facilities closed, while slightly fewer – 40 percent – believe they should be kept open.
In April, by contrast, more Americans supported keeping the prison open (47 percent) than supported closing it (40 percent).
Eight in ten of those who support closing Guantanamo still believe it should be closed even if that means bringing detainees to prisons in the United States.
A substantial percentage of Americans remain scared that closing Guantanamo will make America less safe, however.
Thirty-one percent say closing the prison will make the nation less safe, though that is down from 36 percent in February. Eight percent say the closure will make the United States safer, while 50 percent say it will make no difference.
Four in five Americans are worried about what might happen following the release of Guantanamo detainees to another country.
Forty-one percent are "very concerned" that detainees released abroad will attack the United States in the future, and an additional 39 percent are "somewhat concerned." Just 20 percent are not very or not at all concerned.
In addition, about half are "very" or "somewhat" concerned that former detainees will be tortured or killed abroad.
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No Dent In Obama's Popularity
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Support For Closing Guantanamo Grows
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Though they are split on closing Guantanamo, a clear majority of Americans (68 percent) believe that the detainees held there should either be charged or released. Only 24 percent say they should be held without being charged for as long as the U.S. deems it necessary. President Obama has said a small number of detainees will be held indefinitely.
CBSNews.com editor-in-chief Dan Farber speaks with Sarah Dutton, the director of surveys for CBS News, about the latest New York Times/CBS News poll on Pres. Obama and Sonia Sotomayor:
This poll was conducted among a random sample of 895 adults nationwide, interviewed by telephone June 12-16, 2009. Phone numbers were dialed from RDD samples of both standard land-lines and cell phones. The error due to sampling for results based on the entire sample could be plus or minus three percentage points. The error for subgroups is higher.
This poll release conforms to the Standards of Disclosure of the National Council on Public Polls.