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Unless something "miraculous" happens, the ORFU will tomorrow apply to the High Court to put itself into liquidation.
"There has been meetings going on all day and I'll get a summary if anything has happened," Graham said.
"But it would be fair to say we are not holding out a lot of hope. We have been heartened by support shown but we are still proceeding as we have stated.
"We'll be applying for liquidation on Friday unless something should change in the next [day]. But while I'm saying that, there is a lot of work going on in circles to try and prevent that happening. But unless something miraculous happens, it is probably just about too late."
As well as a $1.2 million bank debt and a $400,000-plus debt to the Dunedin City Council, the ORFU owes $180,000 to 180 local creditors.
Those creditors will not be paid if the union shuts up shop.
That will erode a lot of goodwill in the wider community, especially if the ORFU dissolves tomorrow only to re-emerge under a new name a month or so later with a clean slate.
"[The creditors] are a major concern.. We'd like to come up with some form of solution," Graham said.
"I have a lot of personal friends who are owed money and it does not leave a very nice taste in your month, I can assure you.
"But, at the end of the day, we have to do what we have to do. What I do know is if we are insolvent we cannot continue to operate.
"What the solution is and what the future holds is out of my hands. We are taking advice from rugby union solicitors on what the most appropriate course of action is. But if we allow this thing to continue then, as a business, we are at fault.
"We just have to put a line in the sand and say if we have not resolved it by then, that is it."
Graham has been involved with the union as a player, coach and administrator for the last 37 years and has found the last 18 months distressing.
"It is not pleasant. It has been a big part of my life and a lot of people's lives, I guess. But in the face of adversity, it is what we do now that is important as far as I'm concerned. So whatever is best for the union and for the rugby community is what I'm trying to do.
"The reality is we are going to need a lot of support and it has been encouraging with the indication of support we've had to date. But we've just got to keep working and see if we can come out of the other end of this."