I knew it means 'stalemate' i.e. you've reached a point where no one can win. Why "Mexican" though? For that matter why "stand off"? How did anyone ever find out incorrect facts about anything before the internet? Too much time on my hands again, or to be precise, wide awake at 2am, so I decided to google it….
Wikipedia agreed with the above and also added “In popular culture, the Mexican standoff is usually portrayed as two or more opponents with guns drawn and ready, creating a tense situation.” No real explanation as to the Mexican thing though.
So, much trawling through the internet has led me to the disappointing conclusion that no one really knows what the origin of this expression is. It is likely to have started in the southern US in the late 1800s when all things Mexican were deemed inferior. It would have originally referred to gunfights where no actual bullets were fired and thus were inferior to a ‘real’ gunfight. (I personally like the sound of the Mexican one…) There is also a theory coming out if left field that says it may have originated in 19th century Australia and related to perceived political indecision in Mexico.
Whatever the origin, Mexicans aren’t keen on it and given the whole 'Top Gear' debarcle recently, I think I'll steer clear of using it...