Looking at the most recent DHS yearbook (apples and oranges, but the best I can find so far) at https://ohss.dhs.gov/topics/immigration/yearbook and scaling to match the curve at the ICE stats page, it looks like illegal immigration was way down at the end of Biden's term.
So maybe the influx was already slowed dramatically. I don't think it's possible to stop people from wanting to go to the US, except by making it worse that the places people are leaving. I don't think that's a worthy goal.
This is a classic political tactic to be able to say you want to do something, but never actually have to do it. Politicians use this tactic when they don't actually want to do the thing for some reason. In this case, it's because it's really unpopular with business owners, who like to employ illegal immigrants.
It's perfectly reasonable to say "we need to crack down on employers in conjunction with aggressive border and deportation enforcement". But I'm very skeptical of anyone saying "stopping the flow is step 1". I've heard that story before!