The war would last 20 minutes........Ummmm, maybe not. The perfumed princes would enact ROE’s that could drag out the fight for years.
How an actual war with Mexico would work:
Step 1. Once at war, the US pulls out its CIA and Special Forces assets protecting the Mexican government from the cartels, and leaves them to their own devices
Step 2. Treasury Department cuts off all wire transfers and Western Union payments to Mexico
Step 3. A day or two later, Mexico surrenders unconditionally.