Popeye can advance fairly quickly, yes, but this isn't popeye.
It actually doesn't take that much to build up resistance. When you treat with an antibiotic you kill off the bacteria that is susceptible to the treatment. The first day you kill some, this leaves the stronger ones, the second day you kill off yet another round of more weak ones, leaving ones that are even stronger and so on. Treating for a few days and then leaving it is actually worse than treating a full course. This is why doctors tell you to take the full course even if you feel better and even if the symptoms are all gone. You could have one or two bugs that remain and are resistant and you could pass that on to someone else. Because if there are bacteria there you've just killed the weak ones and left the strong ones to reproduce. This leads to resistance. Bacteria can have multiple generations in hours to days (depending on the species). In some species you can get 100 generations in a day or 2, meaning evolution (the shift to populations with resistant genes) will occur rapidly. This is why the use of antibiotics in countries like the UK (where I am currently at) is heavily regulated. It is not responsible to just throw penicillin in the water.