They survived the potential trauma of being sent down by Hibernian at Tynecastle three days ago, but that was the equivalent of fleeing a firing squad only to jump into an electric chair. If they lose to Aberdeen tonight, again on their home turf, they'll be formally condemned to spend next season in the Championship. Or so they must hope.
It's 31 years since Hearts were last out of Scotland's top division. There will be moments of reflection and solemnity if relegation is confirmed tonight - they are 19 points behind with only six games left after tonight, so it is going to happen soon - but those thoughts will be overtaken by raw anxiety.
Relegation can often act as a form of relief for clubs which have contemplated it for months. Not for Hearts. The timing of meetings in Lithuania to approve a proposed £2.5m Company Voluntary Arrangement (CVA) has nothing to do with the end of the Scottish football season, but the two matters are running in parallel. The next meeting is scheduled for next Monday and a positive conclusion is essential: Hearts' money is running out and their time is too. Around the time they could go down a division they await far, far more significant news from Vilnius.
Playing in the Championship next season looks like a sanctuary right now, a haven which, if it becomes their reality, will confirm that the club itself has survived. The alternative would mean they had been condemned to a deeply uncertain and stressful few months involving failure to emerge from administration, the appointment of liquidators, a desperate scramble to assemble a newco Hearts vehicle, an application for SPFL membership and - if successful in any vote which could involve the likes of Spartans or others competing with them - starting next season in League 2. That amounts to a nightmare scenario which could be worse only if liquidation was followed by no newco at all, and Hearts failing to appear on any fixture lists next season.
Out of the frying pan into the fire didn't quite capture the circumstances faced by the club over the last 72 hours, from the proud defiance of Sunday's 2-0 win over Hibs to the instantly sobering media coverage of the chilling latest twists in the administration saga over the following couple of days. "Obviously, you're on a high on Sunday night, and then the headlines on Monday and Tuesday certainly weren't great to read," said Gary Locke, the manager who can be forgiven for often appearing a forlorn, exasperated figure.
"BDO [the club's administrators] are dealing with that side of things. Hopefully we can get things done next Monday and the club can look to a bright future.
"I spoke to Bryan Jackson [of BDO] last week and he's confident that he'll get the deal done, and that's it as far as he's concerned. We're the same: hopefully we'll get the deal done on Monday and we can move forward as a football club again. I've had a few sleepless nights this season, so that will not change. I'm the same as any Hearts fan. All I want is for the club to prosper and move forward again, and next Monday will go a long way towards proving that.
"I wouldn't say I'm any more worried. I've said all season that the biggest battle we've faced this season is simply being here and keeping the club alive. That's not changed. It's getting closer and we hope we get a favourable outcome, but that's been the case since day one."
What else can Locke and Hearts do but keep calm and carry on, working on the assumption that the club will be spared? Yesterday he announced that his assistant, Billy Brown, will remain in his job until at least the end of this month, having been given another one-month contract extension. That doesn't amount to big news, but it was a sliver of reassurance to a deeply troubled and worried support.
The football has become almost academic to them but, as Sunday proved, it still has the capacity to provide days of glorious relief. Hearts have won only six games in the league this season, yet four of those were against substantial rivals: Hibs and Aberdeen. For all the wildly contrasting fortunes the clubs have experienced this season - Aberdeen are 50 points ahead of them in the Premiership, or 35 even without Hearts' deduction - Locke's team beat them 2-1 at Tynecastle in August and 3-1 at Pittodrie in November.
Perhaps they will do so again, but they have a far bigger battle to win than this.