I think I can; my wife does not think I should.
While I am not the world's best handyman, I do alright with minor repairs, painting etc. I recently replaced the garbage disposal without any issues whatsoever (I know not the most difficult thing either).
My wife thinks I am just going to mess this up and we will need to pay a plumber a lot more than if we just called one to do the job before I mess it up.
I haven't done a faucet before, and while it doesn't look too intimidating, am I asking for trouble?