I'd start by cloning Jeff Cooper, and some of the old school Border Patrol. (just joking)
IMO, one of the best, effecient, and economical ways would be to stop prosecuting ranchers and USA citizens for defending their property and this country aginst the invasion of pagans who are trying to get in.
Another would be to militarily destroy any and all Mexican police and/or military that invade the USA.
Another would be to send in search and destroy missions into northern Mexico (like Israel does against Arab terrorists) to erraticate the gangs of thieves and drug dealers.
A big way to prevent this would be to cut off all funding and services to illegal aliens. We, as the government of the USA, don't owe them anything. Now, I have no problem if you and the neo-conservatives and the bleeding heart liberals get together and start your own private relief fund for them. That's okay. But I don't want my money tax money going to support those who hate our culture and the USA.
The Mexican people have the corrupt government they deserve. Now let them live with the conditions down there or let them change it themselves.
The President is suppose to be a man who is capable of doing the job he was elected to do. Your question suggests that the job of President is too much for GWB. The Constituion clearly states the President is to protect the borders. Maybe the repubs should consider nominating a real man for the job.