"I'm an optimist by nature and I would like to think that we can get something to work, but during the day it's sort of been one step forward and two back, so time's definitely running out," he told Radio New Zealand last night.
Mr Graham said the union would still work on a possible rescue package but he was growing less confident every hour.
"There's a lot of negotiations, it's a very complicated web and it all needs to come together at the same time. And it only will with a lot of goodwill from a lot of different parties."
Otago Rugby Supporters Club chair Fred Cross, who has been involved in the club for over 25 years, said it would be "a sad day" to see the union wind up.
"Otago rugby has been here for a long time, and a lot of people have grown up around rugby in Otago ... To see all their efforts over the years come to this, it's not a very pleasant thing to happen," he told Radio New Zealand.
Mr Cross said one could only hope a rescue deal could be agreed on.
"It is getting late, yeah, but some things are left to the very last minute, you've just got to wait and see."
The impact of liquidation would be felt further down the line.
"There's been a lot of people and businesses that have supported Otago rugby over the years, and it would be a shame to see if any of those businesses are affected by the demise of the Otago Rugby Union."
Mr Cross said something had to be done to try and get an Otago team back.
"We've got to sort out the administration side of Otago rugby and make sure we don't get to this point again," he said.
"It's about getting sponsorship on board, and it's not cheap to run a franchise, so it's about getting that money on board so it can be viable into the future."
ORFU change manager Jeremy Curragh said talks had aimed to get an agreement on a package deal "with all the key parties", and did not involve a request for financial support from the council, but he would not detail what was discussed.
It was revealed this week the ORFU owed the council nearly $400,000 in unpaid rent and other charges for Carisbrook since selling the old ground.
Mr Curragh said there was "a hell of a lot of work going on" ahead of today's 4pm deadline.
"It's got to be an arrangement, and always has been, that works for all parties, and I'm not just talking about the council. That's what we've got to come up with and that's what we're doing."
Mr Curragh said the ORFU's predicament remained serious and liquidation was still the most likely outcome, but "we're going to work right up to four o'clock [today] to see if we can find another solution, and that's what's happening".
"That solution has to be absolutely rock solid... we're working late at night and early in the morning - have since Monday night."
Rugby Players Association chief executive Rob Nichol said the groups would do everything they could.
"We're not going to give up and we're working pretty hard on it."
- OTAGO DAILY TIMES/APNZ
