So the house could have supported no funding for anything that was not part of a deal for shutting down illegal immigration.
There is no enforcement action the House can take to see that the law is followed. You could zero CBP funding and they would just move money from elsewhere to fund sending illegals into he country.
This whole debate is useless and shows how many people just can't realize that this regime is simply controlled by criminals, and in that case, if you want any change you have to remove the regime. No normal legal requirements will work, just like "gun control" laws do not affect criminals.