LAUSANNE, Switzerland -- European diplomats told CBS News correspondent Margaret Brennan on Wednesday that nuclear negotiations with Iran could continue for another 24-48 hours, meaning the talks which have already exceeded their preordained deadline could drag on until the end of the week.
Just hours after the White House issued a public threat to walk away from the drawn-out talks if they failed to make significant headway by the original Tuesday night deadline, Secretary Kerry made an 11th hour decision to stay past midnight and keep the intense negotiations going, arguing that recent progress warranted an extension.
The French, Russian and Chinese Ministers had all left by Wednesday, but in spite of the suggestion the talks could continue for yet another day or two even in the absence of those top officials, Iranian and British diplomats said they were still optimistic a deal could be reached within far fewer hours.
"We hope to wrap up the talks by Wednesday night," senior Iranian negotiator Abbas Araqchi reportedly told Iranian state TV on Wednesday.
"Fingers crossed we'll get there today," Britain's top negotiator, Foreign Secretary Philip Hammond, said Wednesday morning.
Minutes after the midnight Tuesday deadline passed, Kerry and U.S. Energy Secretary Earnest Moniz -- a top nuclear scientist -- broke from negotiations to update President Obama via a secure call to the Situation Room.
Brennan says President Obama's foreign policy legacy could be defined by the outcome of the current negotiations. He has promised not to allow Iran to build an atomic bomb, but major hurdles to the political framework under discussion - which is already more than two years in the making - remain in place as of Tuesday night.
The two sides were still arguing over how much nuclear fuel Iran will be allowed to produce in the future, and how to verify it's for peaceful purposes only, Brennan said. Another challenge is deciding if and when to lift the harsh economic sanctions that have cut Iran off from global markets.
"We insist on lifting of financial and oil and banking sanctions immediately," Araqchi told Iranian TV. "For other sanctions we need to find a framework."
Even if Kerry manages to get a deal, he next has to sell it to some very skeptical members of the U.S. Congress.
Republicans -- and some Democrats -- are preparing a new round of sanctions to levy against Iran if they think the nuclear agreement is weak.
Arkansas Republican Tom Cotton is one of them. Last month, he ignited a political firestorm by sending a letter to Iran's leaders threatening to undo the proposed agreement once President Obama leaves office.
"Unfortunately, it's the president who's putting politics above America's best interest, when he is granting concession after concessions simply on the drive to secure a political legacy as opposed to stopping Iran from getting nuclear weapons," Cotton said.
Brennan says if there is an agreement, Iran's political leaders will have a tough job back home convincing their own skeptical lawmakers that too much wasn't given away in Lausanne. And, of course, their words would likely serve as fresh fodder for the opponents of the deal in Washington.