Carney added that every participant in the diplomatic process had "a stake in seeing it bear fruit."
The warning came as critics of the Obama administration questioned the feasibility of the Assad regime's offer, which came as the president was looking to rally support on Capitol Hill for military strikes in retaliation for last month's chemical weapons attack outside Damascus.
On Tuesday night, the president said in a prime time television address that he had asked congressional leaders to delay a vote authorizing that use of force while he pursued a diplomatic solution.
"It’s too early to tell whether this offer will succeed, and any agreement must verify that the Assad regime keeps its commitments," Obama said. "But this initiative has the potential to remove the threat of chemical weapons without the use of force, particularly because Russia is one of Assad’s strongest allies."
On Wednesday, Carney acknowledged that the logistics of securing the Assad regime's chemical weapons cache in the midst of a civil war remained a daunting task.
"I accept the assessments by experts that this kind of thing isn't easy," he said. "But that doesn't mean we shouldn't pursue it. Because it's obviously a preferable alternative."
The White House spokesman also refused to put any timetable on the U.S. as it evaluated the offer, saying it "obviously will take some time."
"We are doing the responsible thing here, which is testing the potential here for success," Carney said.
Secretary of State John KerryJohn KerryFormer Obama officials say Netanyahu turned down secret peace deal: AP How dealmaker Trump can resolve the Israeli-Palestinian conflict John Kerry to teach at Yale on global issues MORE is traveling to Geneva to meet Thursday with Russian Foreign Minister Sergey Lavrov to negotiate a deal. The State Department said that Kerry will be joined by a team of chemical weapons experts who will help him negotiate the deals of an agreement for the Assad regime to turn over its chemical weapons.
Asked if the United States also risked damage to its prestige if talks fell apart, the White House spokesman sidestepped.
"I think the United States leads in these situation," Carney said. "And it's not always popular and it's not always comfortable. But, you know, we are a unique nation in many ways, the oldest constitutional democracy. And the responsibilities that we bear when there are crises around the world are unique."