Quotas have been ruled illegal in many courts across the country.
The truth is, police managers have used them in the past, and continue to do so today. They don't call it a "quota," and would never admit they demoted, disciplined or fired anyone for not making a quota. (They have. They just would never admit it.)
Police department brass call it "productivity." They say a "productive" officer will get this many criminal arrests, or that many traffic arrests. (They often base this on the average number turned in by any size group of officers.) If you are above the average for the time period -- usually a month -- your bosses love you because you made then look good. After all, when their bosses -- the politicians -- ask, "What are you doing about problem A?" they can say, "My officers made ((number of ) arrests last month to combat the problem."
Meanwhile, if you do not make the average number, you are termed "unproductive." It is said you must be "ignoring" the violations that are certainly happening right before your eyes. Fail to make the numbers for too many months, and you are permanently branded as unproductive, and no amount of good arrests, solving difficult cases, or working on your own time will ever redeem you. When you retire -- if they let you retire -- they'll joke about how you never made a traffic arrest in your whole career. Chances are, they'll get rid of you before you retire -- usually just before.
In the worst case, it has been used as an excuse to fire officers who don't like the quotas or simply excel at the part of their job that doesn't involve getting those numbers.
It's not in all police departments, I'm sure. There is a wide range on this -- some departments that discourage arrests or traffic tickets because they're tourist friendly, others that don't care how many arrests or tickets an officer gets as long as he or she is doing a good job, others who have a number they'd like to see you strive to get each month (usually traffic tickets because that's money in the bank), others who set goals, but don't do anything to enforce them, and others who say, "Get this number, or else."
I have no doubt these officers are telling the truth about what is happening in their department.