Howard Wilkinson told protestors that Sheffield Wednesday "would be in receivership next week" if he and chief executive Nick Parker quit the club.
Wilkinson, 66, appointed interim chairman in May after the shock departure of Lee Strafford, addressed a small group of angry fans who had gathered at Hillsborough during and after Saturday's home defeat to Southampton, which was the Owls' fourth straight loss.
Wilkinson, working tirelessly to attract major investors to help ease the club's debts of more than £20million, said: "If Nick and I walk away, and quite honestly, both of us have got a lot of reasons to walk away, this club would be in receivership next week.
"Now that is the end of the road if that happens, or the beginning of the end, so while we're here, we're fighting for the club you want. So it's down to you. At the moment we're fighting for our lives, but there are people out there who think like we think; whilst ever we're doing that we've got a chance.
"How close are we to investment? We're that close. But it's like those miners in Chile. They're told they're going to get out in November, but they won't believe that until they climb out and see the sun in the sky.
"Now I can't tell you anything. All I can tell you is that we'll keep working at it and try to make it happen."