According to the UN Charter itself, spying would not be an act of war, definitely not a reason to start one. See:
As a practical matter, we cannot allow spying to be considered a reason to go to war, because by it's nature it is hard to prove and easy to fake; it would basically be giving states the right to start a war whenever they want. At times in history we've tried that, such when most of the states of Europe were basically the persons of kings, and it didn't work out so we came up with rules.
This issue is a distraction, as is Private Manning's sexual identification. It just doesn't matter. It is actually the job of the NSA to spy on those communications, and as institutional, political communications they don't have the same moral scanticy and protection as private, individual humans' communications. Prior to Terror being the primary justification, the NSA used to justify some of their actions by saying that they discovered when large foreign contracts had been decided by bribe, and saved American companies the cost of bidding on them; that is also exactly what they are supposed to be doing.
The fact that the NSA got caught, or perhaps even worse yet chose to leak this activity to distract from the fact they got caught in their other activities, is more evidence the agency is out of control and needs to be brought to heel.
In my opinion, the NSA was basically killed by giving it an unlimited budget. Under such circumstances an organization tends to seek out the most expensive, least innovative, least risky things to do and firehose money into them. Take your favorite causes -- defense and law and order if you are right wing, education and health care if you left wing, or your perfered church if you are religious -- and the quickest way to thoroughly destroy that cause is to give it's institutions an unquestioning loyalty and unlimited budget.
In spite of the fact that I think some things the NSA does are good, and perhaps necessary in the long term, I think the best action currently would be to close the whole agency for a number of years. We'd run some risks in doing so, but leaving them on their current path is also running some risks. You can't wave the bogey man of an Islamic Caliphate or whatever and then pooh-pooh the bogey man of a internal Cheka or Stasi. I think if we cut the place down cold, and let the giant glass buildings and huge datacenters collect dust and mold for about 4 to 6 years, we'd be in a better position to restart something smaller and more disciplined around 2020. I think you need to close it for that long, so that all the careerists in there know they have to switch careers and get into other areas. You might end up hiring a large chunk of them back, of course, but half a decade in a different industry shakes up the bureaucratic allegences and gives people a different point of view.