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.
You forgot that Social Security would no longer give the earnings that illegals have withheld from from false SSA accounts but are sent to the Mexican Gubbmint.