The fans' group hoped to discover last Friday that creditors of the club's major shareholder and creditor, UBIG, backed a previously-agreed deal to transfer shares and accept a £2.5million Company Voluntary Arrangement offer. But the decision was deferred until next Monday.
Hearts' situation is clouded by the fact that both UBIG and Ukio Bankas, the second major shareholder and creditor, have also suffered financial collapses and are in the hands of administrators like the club.
And Hearts, who went into administration in June with debts of about £30million, are not believed to have enough cash reserves to see out the season should the process be delayed again.
The Foundation, which is due to take over gradually after businesswoman Ann Budge puts up the initial cash, hopes that creditors of the Lithuanian financial institutions will realise that they cannot get any more money by forcing the club into liquidation.
Murray told BBC Radio Scotland: "I think we are all worried. We want to get this over the line. It has been going on too long now. There have been too many delays.
"There is not enough information coming out of Lithuania. The information that is coming out is inconsistent and incomplete."
The Labour MP added: "We always knew that the meeting on April 7 would determine whether or not UBIG would transfer the shares across to Hearts.
"If those meetings either don't take place, or aren't very positive, then I think everyone has known for some time that liquidation is still a possibility.
"We just have to see what happens on the seventh and if it's delayed a week then that's something we can probably cope with.
"If it's delayed six months, then it's probably something that gives us greater problems.
"It's very difficult to try and second guess. We have all been second-guessing for the last year and it has really not got us any further forward.
"If it happens on April 7, fine, if it doesn't happen, we will need to have a look at where we are and how we take it forward and where the conclusions might lie."
Reports coming out of Lithuania suggest that some creditors have hardened against the deal given the emergence of the involvement of multi-millionaire Budge, whose Bidco company is due to cede control of Hearts once the fans pay back her initial outlay.
But Murray said: "There's a strange irony, that the only people who might be able to buy the club from the liquidators are the supporters and Bidco. So we are running around in circles here chasing our tails.
"It would be much, much better, in their (creditors) interests as well as the interests of the club obviously, to get this CVA process done as quickly as possible, get Hearts out of administration, and enjoy life in the Championship next season.
"If that doesn't happen, a liquidation event puts us back to square one - damaging for the club, very much damaging for the Lithuanians, and very much damaging for the supporters who have done so much to keep the club alive."
Hearts delayed their drop to the Championship on Sunday by beating Hibernian 2-0, but their stay of execution will only last until Wednesday if they lose to Aberdeen at Tynecastle.
And goalkeeper Jamie MacDonald is hoping for another big crowd after savouring the Edinburgh derby atmosphere, despite being on the receiving end of some missile-throwing from the visiting fans.
Among the items that landed in his goalmouth was a training shoe, while a fan was detained after running on to the pitch towards the goalkeeper.
But MacDonald told Hearts TV: "It could be the last derby at Tynecastle for a while and it will be sorely missed by everybody.
"There were a few objects getting thrown my way that I will sell at the car boot sale this weekend.
"But it's good banter, it's all part of football. As long as it doesn't get too serious, you don't mind things like that."
Although Hibs defender Jordon Forster had a goal wrongly disallowed for offside, their fans managed to keep MacDonald busier than the players, who lacked a cutting edge.
"It was probably one of my easiest afternoons of the season, which was great," MacDonald said.
"I'd be lucky if I had one proper save in the game. The boys defended fantastically and it was a great team performance all round.
"That's five or six clean sheets this season and three of them have been against Hibs. If you're going to get them, you may as well get them in the derby."