Only real political pressure would make Washington send troops. I would guess the governors of border states would do something first, like use the national guard.
I don't live in a border state so correct me if I'm wrong but I never hear of border state governors taking a stand against the illegals crashing the border. Some even seem to be in pander mode, for votes I guess.
I do hear them asking for taxpayer money to offset the medical, education, crime, clean up and social program costs the illegals cause the states to incur.