Depends on the size of the garbage? Even paint chips with sufficient relative velocity are a danger to the ISS. The laser would have as much time as it needs to de-orbit something and a limitless power source.
This is to say nothing of the propellant required to transfer the laser-zapper spacecraft into the same orbit as its target garbage.
(Or, for a more speculative take, here: https://childrenofadeadearth.wordpress.com/2016/07/02/the-ph...)