I think I read somewhere that US Presidents have the power to unilaterally sign treaties. I think it came up when Obama was on one of his apology tours.
If that is the case then drawing up a treaty with very specific border control protocols would be the final solution
Presidents can sign any treaty but they only become law if ratified by two thirds of the senate. He can also sign an executive agreement (like nafta) but it needs a majority of both houses. Either can be abrogated by the president without getting approval.
The US Constitution requires a treaty to be approved by the 2/3rds of the Senate, otherwise, a president’s signature is just ink on paper and nothing more.
The reason for this purposely high bar is, once approved and signed, the treaty becomes the law of the land, and MUST be followed.
That might work down the road. Mexico is not likely to sign any such thing. The President of Mexico has to keep the cartels happy or he will not be president long, may even have a short life. He is going to have to keep Trump happy too for the economy of Mexico; but will not do it in public statements or signing a treaty about border security. The cartels essentially have control of Mexico, more so than their government.
Yes, a President can sign a Treaty, but to be lawful it needs Senate approval. I think Obambi's stuff was call "mutual agreements", not Treaties. But then, he did lots of EO's and other stuff to get around US Code and Constitution, not to mention ignoring court findings.
Of course, it was all ignored by the socialist MSM.