You truly underestimate these people. They will surrender, be taken into custody as "captured POW's" and be entitled to everything they're entitled to now as detainees awaiting a deportation hearing except now they'll be war refugees and entitled to much much more. Force only works when you have the authority to use it. If the enemy knows you can't or won't shoot them, it's a joke. So tell me, are you ready to start shooting illegal aliens to keep them out of our country? The reason they all come here without weapons is because they know as unarmed civilians they won't be shot. If they think there's a possibility they'll be shot, they will arm up and shoot their way in.
My preference is a diplomatic edict of economic sanctions on the home countries, Judy's Plan B. Maybe it won't work, but I think it will and it's worth a try over starting a border war with drug cartels and eventually the Mexican and Central American governments. As soon as we fire a shot into Mexico, it's war, and they all know that.
Judy's Plan B:
Tell all these countries, if your citizens don't stop entering our country illegally, then your country will have no aid from or trade with the United States. Period.