But a university town in Massachusetts is doing its utmost to encourage his effort, having become the first in the country to pass a resolution welcoming detainees from the prison on the US naval base on Cuba.
Amherst remains a liberal hot spot in a state that until the shock election of Republican Scott Brown to succeed Edward Kennedy in the Senate was regarded as reliably Democratic.
Unlike Thomson, Illinois, where residents expect a jobs boom from seeing an unused, expensive prison receive detainees judged too dangerous to free, Amherst wants to welcome any former terror suspects who have been cleared for release into its general population of 34,874.
It has set its sights on two men in particular who are languishing in Guantánamo unable prevented from returning to their home countries by the likelihood of maltreatment.
Ravil Mingazov, a former ballet dancer in the Russian army, said he was persecuted by the authorities because of his conversion to Islam. He travelled to Afghanistan in 2001 before his arrest in Pakistan in early 2002.
Also handed over to the Americans in Pakistan was Ahmed Belbacha, a 40-year-old Algerian accountant. Though deemed not to be a threat by the Pentagon in 2005, he asked to stay in Guantánamo because he so feared torture by his country's security services. His lawyer has said he "would love to move to Amherst".
For that to happen, Congress would need to reconsider legislation preventing detainees with cleared status settling in the US, a decision that has contributed to Mr Obama missing his deadline. But with dozens of detainees probably moving into detention in Illinois, that could be changed.
Mingazov and Belbacha "would be a great addition to the community, and both are able to work," said Ruth Hooke, 82, a staunch supporter of the motion passed by the town council.
Observing that Mingazov was "an ardent Muslim", the retired university teacher said: "We have a mosque here in Amherst, so he would fit right in".
Gerry Weiss, a member of the town's select board, or executive committee, compared Amherst with a town in occupied France that sheltered 5,000 Jewish people during World War Two.
Others were appalled at Guantanamo's legal regime, which has incarcerated innocent men for years and brought only a handful of terror convictions.
Nancy Talanian, director of No More Guantanamos, said the motion was "a wonderful message for Congress and the world that there are communities that are willing to stand up for what is right".
Some residents however believe the motion is profoundly wrong. Stanley Gawle warned that if any detainee from the US prison on Cuba moved to Amherst he would start carrying a gun.
"I feel that our government is in a hurry to clear Guantánamo out, and I have reservations about how thorough the clearing process is going to be," he said at the meeting that passed the resolution.
Stephanie O'Keeffe, the only select board member to oppose the motion, thought the closure of the world's most notorious prison was simply not within the purview of a small town's ruling body.
"We all have opinions for sure, but that's not the same as having real information for careful decision making. This is somewhat beyond our expertise," she said.
Angry, prospective parents have called her threatening not to send their children to Amherst College, a private law school regarded as one of the best in the country.
The 240-member town council has previously voted to impeach former President George W Bush and vice president Dick Cheney, called for an end to genocide in Darfur and in urged the government to pursue diplomacy with Iran.
The town's name is properly pronounced "Amerst" - without the "h". The bumper sticker most commonly seen around its quaint, collegial streets reads: "Amherst: Where Only the H is Silent".