The American Veterinary Medical Association reports that 57% of US households own pets. Considering just dogs and cats (most pets are either dogs or cats), on average there are two pets per household. According to the Oklahoma City Chamber of Commerce there are 280,308 households in Oklahoma City. A rough estimate of the number of pets in the city is 319, 551 (0.57x2x280,308). Central Oklahoma Human Society reports for 2007 that approximately 28,000 pets were taken in at the shelter.
Thus, only 9% of the city's pets went to the shelter last year. I agree with you that is too many irresponsible owners, but it clearly isn't appropriate to characterize pets owners as irresponsible in general. In fact it is more appropriate to say that the vast majority of pet owners are responsible.

Oklahoma city municipal code state that "No person shall harbor or keep dogs or cats totaling more than four of each over the age of six months in any household." Each household can have eight pets. The total number of pets the city can house is thus 2,242,464 (8x280,308). The city is at 14% capacity. We are no where near flooded with pets.