The Gorgie club entered administration last month, which brought a 15-point deduction and a registration embargo with further possible sanctions to follow.
Manager Gary Locke has watched a whole team of players depart the club, including experienced defenders Andy Webster and Marius Zaliukas and striker John Sutton, and has been left with a squad packed with youngsters.
Wilson, 21, who will take over the armband from Zaliukas for the forthcoming campaign, believes surviving in the top flight would ensure their places in Jambos folklore.
"I think it would be the biggest achievement in the club's history if we were able to overturn this," the Scotland defender said.
"We are young and it is going to be difficult but we have the chance to make ourselves heroes at this club and that's what you want as a footballer.
"You would rather be going for cups and titles, obviously, but this would be just as big.
"It is a great opportunity for all the young boys. They will be playing every week and, at their age, that doesn't happen in many teams.
"This is a massive club and, if they can do well this season, they can become heroes at a very young age.
"We have to have the mentality that everyone is against us and we are going to go out there and prove everybody wrong. It is the only way we can approach every game.
"We have nothing to lose this season - we are already 15 points down."
Some eyebrows were raised when Wilson resisted the temptation to join the Tynecastle exodus.
The former Rangers player agreed a three-year deal with the Jambos following a loan move from Liverpool last season but could have moved on when Hearts entered administration.
A loophole allowed him to get around the consequent signing embargo imposed but, along with several other players, he took a wage cut to stay at the club.
Asked if it might have been better to go somewhere more stable, Wilson replied: "People have said that to me and I had other offers but I made the commitment about a month and half ago to stay here and I made a lot of changes in my life for that.
"I had bought a house and was settled and didn't want to uproot again.
"Obviously, I took a wage cut to stay and was more than happy to do so to help in any way I could.
"I had been really happy here for six months and I get on so well with the manager and the boys at the club.
"So you don't just trade that for a bit of uncertainty.
"I'm here for the long haul and hopefully we can come through this better."
And Wilson is "really proud" to be the new Gorgie skipper.
He said: "If it was a few years ago, when there were more senior players it wouldn't have happened, but the gaffer has given me the honour of being captain.
"But even if anyone else had been given the captaincy, we all need to show more leadership this season."
Meanwhile, the Foundation of Hearts has confirmed a partnership with Gordon McKie's consortium is one of two options for its impending takeover bid - but the fans' group is set to take an alternative route.
Former Scottish Rugby Union chief executive McKie admitted today that his group of Hearts-supporting businessmen could not fund a takeover alone.
The Foundation of Hearts confirmed McKie's proposal was welcomed and is one of the two options they referred to 24 hours earlier, which both involve supporter investment in partnership with business.
But the network of fans groups added in a statement: "At this time, the Foundation is set to choose the alternative funding option but wishes to maintain a strong, positive relationship with Mr McKie's group, given it and his own personal expertise."
The group reported a 15 per cent increase in fans converting their pledges into direct debits in the 24 hours since the launch of their "final push" - a number which sends them towards the 5,000 mark.
Foundation of Hearts chairman Ian Murray MP said: "The board of Foundation of Hearts will consider the best option for Hearts - nothing else - ahead of next week's deadline.
"We welcome Gordon's honesty that his own consortium is not in a position to go it alone and thank him for putting a proposal to us. They have been forthright and professional all through the process.
"Our bid will combine capital funding support alongside the fantastic efforts of supporters in setting up thousands of direct debits to the Foundation to provide a stable ongoing financial platform."