It's called an "invasion".
Perhaps this has gone beyond the level that a "government agency" can handle any longer. Homeland Security -- it's now out of their level of competence.
Perhaps it's time to TREAT IT "as an invasion", even if the invaders don't wear uniforms and aren't armed (although a few of them may be quite armed).
That means PHYSICALLY OPPOSING their crossing, and using those means that would normally be employed to stop invaders from invading.
We either do that or build a border barrier.
One or the other (actually, both).
Otherwise... the country is lost.