It depends.
A few assumptions to make the math a little easier for me: GME opens on Monday morning at $300 per share. During Friday's trading, the hedgies somehow buy enough GME to bring the short float down to 100% by Friday's closing bell, meaning that Friday's after hours and Monday's pre-open trade is just shuffling deck chairs on the Titanic. Melvin Capital is reportedly on the hook for $1b for every $12 over a $20 share price (let's assume that all the other shorts have buggered off and decided to let Melvin take one for the team).
$300 - $20 = $280
280/12 = 23.33
viz. the shorts would be about $23b in the hole in this example.
Given that some of the larger hedgies have trillions in assets, even a loss of $20+ billion is a drop in the bucket for the overall market.
Bear in mind that this is a very simplified explanation, and doesn't include other factors such as interest paid on shorted stock. Please let me know where/if I've fucked up.