Nah, they have enough time. The game was designed with the assumption that the users split the keys into batches (or singles), so multiple ppl can test keys at once. passing them in a circular fashion. Mc is just very dumb for someone who won 28 times (I would prolly be similarly dumb under that stress, but the point is that she is supposedly not particularly stressed).
Potentially also assuming that they eliminate used keys from the pool, but that in itself might be a mistake (maybe all handcuffs uses same key?).