So what’s going to happen when they all show up at the border claiming asylum? Don’t we by law have to let them in?????
They will try and overrun the checkpoints and nasty violence will ensue.
All the vetting necessary would be done, and the obvious fails sent back to their home country forthwith.
The borderline individuals would be held, together with their family units, until satisfactory histories could be worked up on them, or they proved to be phonies also. There may be a VERY small sliver who qualify for "refugee" status, but after Mexico has offered then asylum, and they refused, it is WAY much harder to make their case.