[quadragenarian]

As mentioned in the article you linked, the president has a veto over any law to restrict his own tariff powers; the only way to override his or her veto is to pass the law with 2/3rds majority in BOTH chambers, the House and Senate.

That does mean a fair number of Republican Congresspeople would have to join Democrats. This level of cooperation seems to be in itself anathema to Republicans, notwithstanding the actual principle of the bill itself.