You establish a random circuit through the Tor network when you first connect. Even if the NSA is analyzing every packet between every node, they're not going to be able to distinguish your packet from anyone else's. I think they would need to control some of the nodes to keep track of packet sources and destinations.
You are wrong. Tor does not include any latency, so a passive global adversary who can watch every packet can correlate your input to the Tor network with the traffic between nodes and the outputs of the exit nodes, and thus break the anonymity property. The reason this does not apply to anonymous remailers is that they randomly permute the messages they receive, sending them out in a different order than they were received; this creates far too much latency for use with HTTP or IRC or other common protocols, so Tor sacrifices security against a global adversary.