FILE - This undated photo provided by the U.S. Army shows Sgt. Bowe Bergdahl. (AP Photo/U.S. Army)

Fifty-six percent of Americans say the U.S. paid too high a price to secure the release of Army Sgt. Bowe Bergdahl, a new CBS News poll released Tuesday shows.

Among veterans, the percentage saying the price was too high rises to 65 percent. Overall, a 45 percent plurality of Americans say they disapprove of the deal and 37 percent say they approve.

Bergdahl's release from Taliban custody was secured last month in exchange for the release of five Taliban commanders who had been held at Guantanamo Bay. Some lawmakers have criticized the Obama administration -- both for not informing Congress in advance and of setting a precedent they say could put U.S. troops at risk in the future.

The CBS News poll comes a day after a USA Today/Pew Research Center survey showed 43 percent of the public saying they disapprove of the deal and 34 percent saying it was the right thing to do.

There is a partisan divide when it comes to opinions of the deal, the CBS News poll shows. While most Republicans say they disapprove of the deal, a majority of Democrats say they approve of it.