If thou canst believe, all things are possible (Mark 9:23)
Extra-Biblical sources indicate that some of the Israelites refused to look at the serpent; clearly they did not believe it would work. This is implied by the account in Numbers which specifies that it was those who looked (rather than saying "everyone") who were healed.
Among those who did look, there is no indication that the remedy was anything less than 100% effective.
The strong implication then is that both of these statements are true:
Look -> Healed (if look then healed)
~Look -> ~Healed (if not look then not healed)
Looking, therefore, was an act of faith. It does appear (pun intended) to be a very simple act of faith, but then again, how many of God's other teachings are simple...and yet often discarded?
God gave the promised blessing to those who believed sufficiently to act on the instructions He had given through His prophet. This passage is an extremely literal example of the teaching given by James: "faith without works is dead".
It is unclear how much travel was expected of the ill--did they have to go somewhere specific to see the serpent? This is easier to imagine than people having the serpent brought to them and shielding their eyes lest they look upon it, but we are not told.