What they fail to mention in most of these articles is that fast track also changes the requirement for treaties from 2/3rds to a simple majority. This trade agreement will never happen without fast track. If TPA (fast track) is passed there will be no other debate and TPP will become law. It may even allow a few Senators to be on record voting against it knowing full well that it will have 51 votes anyway. I suspect that Cruz will be in this category since he already voted for fast track.
It is impossible for the Senate to pass a treaty with a “simple majority.”. The Constitution forbids it and Senate rules don’t trump it.
What a “simple majority” allows is no immediate hassle with the bill and the ability to undo it whenever the Senate so deems.