The fact of the matter is (and I came across this argument a couple days ago on an unrelated matter) that Congress has the authority to grant (and remove) the fast track power. Some people believe that when the Constitution gives the authority to Congress to "regulate commerce" between foreign nations, that authority is limited, which places them in the uneviable position of arguing that the authority is not really authority (limited vs. plenary). As soon as that argument is made, a departure is made for uncharted Constitutional waters.
So what happens if, after the appropriations bill becomes law without funding the Mexican trucks, the NAFTA arbitration panel awards damages against the US government? Suppose congress refuses to authorize money for the award?
My opinion is that congress should amend the NAFTA authorization law to put limits on what damages the US will honor. In this case, the panel could award damages even though Mexico has no legitimate and effective tracking of driver records, so allowing Mexican trucks in will endanger public safety and perhaps national security.
Also, I am not a lawyer, but perhaps there would be a way to challenge such an award in the courts on the grounds that the safety concerns outweigh any arbitration panel’s decision, although I don’t know exactly what legal arguments would be used.