The War in Iraq lasted 8 years and cost over 1 trillion dollars.
So aside from the immense risk of starting a war with a nation right next door to you, ...aside from the fact that there would be no clear strategic objectives, it would also cost a fortune.
If the US wass really serious about supporting the Mexican government against the cartels, then they would start with increasing financial aid to said government. But these very same people would probably be against that idea.