Hearts have warned fans the club might not survive until the end of the month after being hit with a winding-up order over a tax bill of almost £450,000.
The Clydesdale Bank Premier League club issued a plea for "emergency backing" after confirming action by Her Majesty's Revenue and Customs at the Court of Session in Edinburgh.
Hearts said they were attempting to negotiate a payment plan with the tax authority over the matter, which is unrelated to a £1.75million HMRC bill the club are challenging at a tax tribunal.
But they later asked supporters to find the money to see the club through the crisis in an appeal described as "not so much a request as a necessity".
Hearts urged supporters to buy tickets for forthcoming home matches and invest in a recently-launched share issue.
The board statement added: "Without the support of fans there is, as we issue this note, a real risk that Heart of Midlothian Football Club could possibly play its last game next Saturday, 17 November, against St Mirren.
"This isn't a bluff, this isn't scaremongering, this is reality."
New SPL rules introduced in the summer would see Hearts face a more stringent punishment than the previous automatic 10-point penalty if they are forced into administration.
The rules state Hearts would be deducted a third of their previous season's tally, rounded up to the nearest whole number. Hearts finished on 52 points last season, which could mean an 18-point deduction in the coming weeks.
It was court action by HMRC that forced Rangers into administration in February.
The statement added: "Without your help now, we could be entering the final days of the club's existence.
"There are limited options for the board of directors to take to avoid the catastrophic consequences that a funding shortfall would mean for the club.
"In a footballing sense alone Hearts will suffer an immediate 17-point (sic) penalty.
"This would just be the start of a painful process that will affect every one of us and could lead to far more damaging actions that threaten the very existence of the club."
Hearts earlier said they were "endeavouring to agree a suitable payment plan with HMRC for the outstanding amount of £449,692.04" and that the petition had only recently been presented.
A club spokesperson added: "We have guaranteed future revenues from forthcoming games and related broadcast income as well as additional guaranteed transfer income which will more than cover the outstanding amount stated in this petition.
"We would therefore be hopeful that HMRC will accept that winding up the club would be totally unnecessary."
But the tone became significantly more desperate in the subsequent statement.
Hearts urged fans to buy tickets for home games against St Mirren, Celtic on November 28 and Aberdeen on December 8.
They also continued their attempts to persuade supporters to sign up for the share offer.
"There are risks, we know, and these are laid out clearly so be very sure this is right for you before committing but please at least consider it," the board said.
"Discussions on whose name is above the door, talk about how the money has been spent and debate on whether the investment in silverware has been appropriate is all natural but quite simply worthless at this moment in time.
"The only valid debate now is how can you help the club. Is the club worth less than £110?"
The board said they would continue to seek the support of parent company UBIG, Vladimir Romanov's investment group, but the club has been moving towards a self-sufficient model.
The Scottish Government pledged to help Hearts find their way through the crisis.
A spokesperson said: "The Scottish Government stands ready to assist in any way it can, including making contact with HMRC if necessary.
"It is in everyone's interests to find a solution which ensures that Hearts can continue in business while also meeting their obligations to the tax authorities."
Hearts launched a £1.79million share issue two weeks ago but the prospectus revealed another tax dispute.
HMRC has claimed unpaid tax liabilities in the region of £1.75million relating to loan agreements for a number of players who joined Hearts from Lithuanian club Kaunas, who were then run by Romanov, the Tynecastle club's majority shareholder since 2005.
Hearts claim the situation was no different to other loan agreements when parent clubs pay some or all of the wages, and will contest the bill at a tribunal this month.
The winding-up order is not the first to be issued to Hearts by HMRC.
The club announced in February they had paid an outstanding tax bill after being given eight days to pay or face being wound up.
Last year, Hearts were forced to pay a bill in the region of £500,000 to defeat a similar order, while others were served in 2009 and 2010.
The club have faced growing problems meeting wage bills in the last 12 months and are currently under an SPL transfer embargo following consecutive late monthly payments to some players and coaches.
This came despite the club reducing their wage costs significantly in the summer with the departure of a number of experienced players.