Bryan Jackson and Trevor Birch from administrators BDO told the Jambos support last Friday that the stricken Gorgie outfit faced a £750,000 funding gap and warned they would have to push sales of season passes up from 7,000 to more than 10,000 if the club was to survive.
Since that appeal went out a week ago, fans have snapped up more than 1,500 season tickets.
Birch said: "Selling in excess of 1,500 season tickets in just over a week is hugely encouraging - and all the more impressive when you remember that fans have only been able to buy tickets in person by cash or cheque at the ticket office.
"The response has been tremendous and we are grateful to everyone who has supported the club. We're not out of the woods yet but every ticket we sell buys us much-needed additional time to secure the club's future. We're all heading in the right direction and we need to keep the momentum going."
Meanwhile, former Gorgie favourite Paul Hartley has told the club's faithful they have the right man in charge in boss Gary Locke.
By calling in the administrators Hearts triggered a 15-point penalty and transfer embargo, while first-team players Ryan Stevenson, Jamie MacDonald and Jamie Hamill have all accepted 50 per cent wage cuts.
But Alloa manager Hartley believes having Locke in charge is one thing fans can be positive about.
He told Press Association Sport: "The fans have been great, as have the players by taking wage cuts. And it will be difficult on Gary too. All he will want to do is manage the team, to try to get a good group of players into his squad so they can have a successful season.
"But he has got a transfer embargo, a young squad and he doesn't know which players are coming or going. They will be starting the season minus 15 points, so it is testing for him. But I know Gary well and the way he has handled himself has been terrific. The fans and players are right behind him and he's a true Hearts man."