Our friends at Tricycle will push through a zero-based karma system (no self-voting possible) sometime this evening. At present this will only cover future posts/comments - they may go back and revise history some time in the indefinite future (or not), but apparently that would be overly complicated for now. We'll see how this works.
Then it should be possible to see how many down votes I've cast, to know how many are left. In practice, I expect that the number of downvotes is significantly less than the amount of Karma, but I'm not sure. If this is true, then the limitation is roughly equivalent to simply prohibiting people with Karma less than a threshold to downvote.
You are notified when you reach the limit by a message stating how many down votes you've made and what your current karma is. Until then I imagine you should not let this limit influence you:
Note: It is possible to see this message and the down vote count be greater than the karma due its dynamic nature.