Update as of Season 7, Episode 7.
There are hundreds!
The official script for Season 7 Episode 7, "The Dragon and the Wolf", has been released because it is up for an Emmy.
[EXT. EASTWATCH, NORTH SIDE OF THE WALL]
Emerging from the frozen coastal forest, the ARMY OF THE DEAD comes in force. All of them, 100,000 strong, with hundreds of WHITE WALKER officer corps on their dead horses.
Yes, the Night's King can create more, as seen in S4E4
Since this is a living human being turned, it becomes a White Walker. The Wights are reanimated from those already dead.
The problem with this now is that it seems the source for these babies was Craster (who before that we are unsure). Since Craster is dead now it might a be bit harder to come across a steady supply of living human baby boys.