Dick Durbin, a senior Democrat senator, said Obama had put Democrats in an awkward spot by asking for funding without an accompanying plan.
"The feeling was at this point we were defending the unknown," he said. "We were being asked to defend a plan that hasn't been announced."
The senate, however, took up the US president's request for money for military and diplomatic operations in Iraq and Afghanistan.
Democrats in the House of Representatives last week also dropped funding to close Guantanamo when producing their version of the war funding bill, which was easily passed.
Obama is facing pressure from US senators, particularly Republicans, who have made it clear they do not want any Guantanamo detainees sent to the US to stand trial or serve prison terms.
|Rights groups have long alleged abuse and torture at the Guantanamo prison [Reuters]
Robert Gibbs, the White House press secretary, told reporters that legislators were correct to insist on details on closing the detention facility, saying that Obama would outline "a hefty part" of his plan on Thursday.
Rights groups have urged Obama to move swiftly on shutting the prison, widely condemned by the international community for alleged abuses.
In recent weeks, Eric Holder, the attorney-general, had sought to reassure sceptical legislators but congress appears unconvinced and may force the detention facility to remain in operation.
Under the separation of powers outlined in the US constitution, congress has control over almost all of government spending, and can therefore stop virtually any programme by refusing to fund its implementation.