Here rests problem two. Problem one, the hand counting. Now that it has started it must continue. Problem two, absentee ballots. Recount numbers notwithstanding, there are enough absentee ballots to change the outcome of the Florida election and, perhaps, elect a new president.
Nobody can claim victory until all of Florida's votes are counted.
Finally, what is going on is not a threat to our republic. If anything, this strengthens it. Whenever a recount is triggered, whether it is a situation such as Florida's or whether the recount is for the election of a low level city position, there is a process. There are counts, challenges, and maybe even judicial intervention, but there is a method to the madness. In Florida, the process will work.