He probably didn't expect anything unconstitutional to be going on when he took the job.
I checked the NSA oath, it doesn't say anything about the constitution. But if he ever said the pledge of allegiance, he swore allegiance to "the Republic for which it stands". And that would be an oath to uphold the constitution.
The "proper channels" were aware that the unconstitutional snooping was going on. They were part of the problem.
So he went to the next proper channel, the U.S. press which refused to touch it because it's bought and paid fork, so then he went to the British press and many Americans are thankful.
(/s)
He's a lawbreaker. It's not up to him to determine the Constitutionality of the laws. He can go to court to challenge them of course ~ as can anyone.