Running an airline is a bit like a confidence game - you have to persuade people to give you money now in exchange for the promise of a flight in the future. While customers are confident they give you the money; when confidence goes the airline had a problem.
Thomas Cook a few years ago had a similiar problem - they managed to regain people's confidence in their finances.
Monarch right now needs to be able to demonstrate that a backer has put tens of millions of pounds into Monarch's bank account and then go through the
PR media circus of a few suits shaking hands (one of which being the wealthy investor). The cash influx needs to be large so Easyjet / Ryanair / Jet2 believe that Monarch are able to fight back if necessary against a price war. If these two things happen, confidence will quickly return and everything carries on as normal.
Monarch are fortunate that now is not a critical booking season lfor holidays - things would be worse if this was happening in January. Most retail consumers have short memories of corporate events; Monarch need to get the whole thing resolved quickly but if they do then bookings will bounce back.