More than 100 passengers were due to fly at 11:00 BST on Monday, but were told their flight was going to be late due to a "technical fault".
The flight, operated by Lithuanian airline Small Planet, was cancelled several more times and is now scheduled to leave at 00.55 on Wednesday.
Small Planet said: "We have never had such a difficult situation before."
Manchester Airport confirmed the delay was the longest passengers have had to endure at the major travel hub.
Passenger Paul Kenny booked the flight through tour operator Olympic Holidays.
He said the 11:00 flight on Monday was initially postponed until noon and it "constantly got delayed and delayed" until about 20:00 last night "we were informed we had to stay in a hotel".
He said the situation had been "awful".
Kevin Clarke, from Bott & Co Solicitors, said Small Planet had a history of not paying compensation claims and one of its planes had recently been seized as a means to force payment.
"We've invited them to settle claims, we've issued court proceedings, we've even had courts order them to make payments and unfortunately they're ignoring those court orders and they're still not making payments," he said.
He said the law firm waited until they "had an asset in the UK, which was an aircraft" and obtained a court order to seize it at the airport.
"So when the plane landed on the runway, the officer of the court was there waiting for it and took ownership of the aircraft and so they paid their debts... they had no option."
Dave, another passenger caught in the delay, said: "We're angry, we are just not being told the truth.
"We're told planes are on the way, but they never turn up. It's frustration."
A Manchester Airport spokesperson said: "Small Planet Airlines flight to Corfu is currently still showing as delayed until tomorrow morning.
"In the meantime we will work closely with our terminal teams and handling agents to ensure the passengers are cared for and looked after, until their flight to Greece can depart."
It is believed a plane is being flown over from Lithuania to take the holidaymakers to their destination.
Flight operator Small Planet issued an apology on its Facebook page.
It read: "Dear passengers, we sincerely apologise for all the inconveniences and stress that current flight delays from Manchester to Corfu (S5 0111) and Corfu to Manchester (S5 0112) have caused you.
"Please, rest assure that we do everything we can to eliminate the technical issues."
Holidaymakers hoping to get to Corfu for some summer sun are facing a 38-hour delay at Manchester Airport.