It honestly depends on what sort of programming you're doing.

If you're making light web apps with some logic, you probably don't need the more advanced math classes that many degrees require. If you're working with things that are a bit more processor heavy, than you're going to need more math. If you're doing work with any kind of scientific field, you'll really want to keep your calc references at hand.

Another place where you'll need math is if you want to write games. The second you want to move diagonally, you'll need to start doing some careful calculations so that you don't end up with characters that accelerate if the move to a block to the NE.

That said, you don't necessarily need to learn math, then learn programming. It's perfectly valid to learn programming, then pick up some advanced math. I started coding before I ever set foot inside a Calc or Trig class and did just fine. When I did start learning advanced math, I found that coding really helped me, as I could explore the topic more by changing variables in a quick script than I could with pen and paper.