Yes, but only in the area of REDUCING tariifs - not in raising them.
"The Act served as an institutional reform intended to authorize the president to negotiate with foreign nations to reduce tariffs in return for reciprocal reductions in tariffs in the United States."
"Another key feature of the RTAA was the fact that if Congress wanted to repeal a tariff reduction, it would take a two-thirds supermajority."
And even if the president negotiated a change in tariffs, it had to be approved by Congress - a reduction in tariffs only required a majority vote, but an increase required a 2/3 majority.
There are so many ways around that.
Just one. The day Trump is elected, due to national security issues, we might be required to search every single vehicle/truck crossing into the U.S. I imagine it would back up traffic from from our southern points of entry to Mexico City. But national security is top priority.