Most soldiers would have a hard time machine gunning women and children. Not really worth it either. Build a wall (and not a chintzy one either), put some landmines in front of it, give significantly more leniency in the rules of engagement, etc.
The biggest problem is not the border. There are three problems that are the cause. One, employers who hire illegals. Two, welfare state. Three, the corruption and other general problems in Mexico.
So let's stop just focusing on the border. Crack down hard on businesses that hire illegals, to include direct criminal charges for managers, HR and executives. With immunity if e-Verify screws up, not them. Gut the welfare state or require proof of citizenship for using social services. As for Mexico, I dunno what would help short of drastic measures that are politically unacceptable.
+1. As far as the last sentence, I also "dunno" if it would be politically viable, but I'd like to see illegal Mexicans awaiting deportation being educated in the topic of what in my high school education would have been called "government" or "civics", and in my college education called "political science", in the hopes of planting seeds of a future Mexico NOT being ruled by the thugs that have ruled it for centuries.
There's no geographical reason why Mexico couldn't be as prosperous as the United States or Canada. If it were, we'd have no more reason to fear Mexican illegal immigration than we do Canadian illegal immigration (other than that of potential Jihadists), in other words, very little. The reasons they aren't as prosperous as us are all human and political.
