The poll found that 56% oppose shutting the center, while 40% support the idea.
The support for keeping Guantanamo Bay open is driven largely by Republicans, with 83% saying it shouldn't be closed -- up from 76% in August.
Obama last month unveiled a plan to close the prison
and move the bulk of remaining detainees to other countries or to an as-yet-undetermined detention facility in the United States. Congressional Republicans oppose the idea.
Americans now see North Korea as one of the nation's biggest threats, on par with Iran, but their concerns about Russia and China are waning, according to the same survey.
The poll found that 44% of those surveyed see North Korea as a serious threat, up from 37% last September and 32% last April. North Korea launched short-range projectiles Thursday
, and the United Nations' National Security Council voted earlier to impose sanctions after the nation's most recent nuclear test and missile launch.
Fears about Iran, meanwhile, are moving in the opposite direction, with Americans less concerned about the country since the nuclear agreement took effect -- 43% call Iran a very serious threat now, down six percentage points since September. Concerns about China and Russia have also waned, with 28% and 27%, respectively, saying they are concerned.
Combat roles for women
On the issue of combat roles for women, younger Americans are more apt to say that women should receive the same assignments as men than older Americans, with 47% under the age of 35 approving, compared with just 25% of older Americans.
A majority of Americans also say that if a military draft is reinstated, young women should be required to participate -- 54% said yes, 46% said no. But only 1 in 5 Americans said the U.S. should reinstate the draft.
The CNN/ORC poll of 1,001 adult Americans was conducted by telephone between February 24 and 27. Results from the full sample have a margin of sampling error of 3 percentage points; is is larger for subgroups.