I don’t have a cite as it was a few days ago, but I read that with the Democrats in control of the House the UK has to treat Ireland with respect as there’s many pro-Irish Representatives in the House who would play havoc with a Trump trade deal. Whether that’s an accurate portrayal isn’t the issue here.
But to my knowledge, treaties are the exclusive bailiwick of the Senate, according to the Constitution, is that right? What can the House do to exert influence?
Trade deals are not treaties in the US, but laws. The House of Represenatives has debate and a vote on trade matters just as the Senate does. These are generally up-or-down votes, with no amendments allowed. And of course, it requires a majority in both houses to pass a law, instead of the 2/3rds of the Senate that’s required for a treaty.
The power to “regulate Commerce with foreign Nations” is given to the whole Congress.
Also “treaty” has a pretty fuzzy definition under US domestic law, and sometimes things that are seen as binding treaties in international law are “executive agreements” or “congressional-executive agreements” in US law.
That raises a question: if trade deals are enacted laws of the United States, how is it that Trump can threaten to unilaterally “pull out of NAFTA”? Wouldn’t he need Congress to repeal the enacting legislation?
While I think I have a pretty good handle on questions regarding withdrawal from treaties, I’m not really familiar with laws on withdrawal from trade agreements. But it appears to be a difficult and controversial question: link.