Currently there is no law that says (where I live) that I cannot
> program a computer to call numbers looking for fax machines.
I am not a lawyer, but I believe what you propose to do IS indeed against federal law. It absolutely is against the law to call certain restricted numbers or a line under monitor without legitimate purpose (and a review of your call out log would show that it wasn't legitimate).
As to calling government offices, you may find yourself visited by a government employee who will invite (decline not an option) you to come with him or her to discuss the matter further.