I believe that the issue is not as bizarre as it seems. The US had been invading Mexico on and off since 1914, and for their part Mexican 'parties' to the infighting there had spilled over the border on several occasions, leaving aside the likes of plan San Diego. By mid 1916 the US had enacted legislation to expand its military, had mobilised all 12 NG divisions on the Mexican border and was undertaking the Punitive Expedition with 1 of the 3 Regular Army divisions. From this perspective the US - Mexican relationship was virtually in a state of war anyway, actual war would be worse by degrees rather than breaking a nice comfortable peace, so the step is not massive.
Another factor is that the RN was getting something like 70-80% of its oil supplies from Mexico. Apparently there was a plan or idea in place for the US or Britain to seize this oilfield if events in Mexico threatened to disrupt supply of oil. Again, when coupled with the Punitive Expedition, this threat shows the pressure Mexico was under from the US and Britain as well I think. So talk of war isn't some crazy idea out of nowhere, it fits the situation at the time.
I believe that if Mexico did go to war then she and Germany would only be nominal allies. Mexico would cut off the oil to Britain and Germany would send what support she could, perhaps Uboats to operate in the carribean.