One of the biggest misconceptions out there is that you are interviewing people for "quotes." You are interviewing people for information around which you can build a good story. Yes, you can overdo it because of the opportunity cost of conducting interviews for a single story. Time is finite, particularly in daily newspaper work (as opposed to books and magazines, where you have more time to follow dead ends). That being said, in theory you can't overdo it, because every person you speak with has the potential to add something to your piece.
Just don't feel obligated to quote every one of them.
Always remember that you are collecting information, not quotes. Some of the biggies in the business quote sparsely, if at all.