Claverhouse,
Oh I fully understand why the Germans would want Mexico to invade. And the pre-WWI US army was absolutely tiny. But the Mexican army wasn't that much bigger, and despite years of intermittent civil war doesn't seem to have been particularly effective or done much with all that potential combat experience. Plus I think the Mexicans got a lot of their weapons from the USA - and the Germans were in no position to ship them any.
As I understand it the Mexican government came to that conclusion pretty quickly, and also wasn't particularly optimistic about holding on to Texas even if by some miracle they were able to take it and hold it long enough to get it in the peace talks (should the Central Powers win).
Hence it's such a transparently bad offer that there seems no possible reason to take it. Or in fact to do anything else than try and win brownie points from Washington by telling them all about it.