With American Airlines, you can pay for your flight in pesos at their office in BA (with U$S 25 fee). They convert the USD price at the official rate, so if you have dollars that you can exchange at the blue market rate or get from Xoom, you'll save a decent amount.
The other option is to sign up for a credit card with airline mile signup bonuses and get your flight on miles. A lot of these have minimum spending requirements, but there are a bunch of tricks to meet those (including paying a partner through Amazon payments, etc.). I just flew my mother-in-law business class to the States for $1800 by buying miles, and we're flying coach for 20,000 miles each way.
As an example, the Starwood Preferred Guest Amex is now offering a 30,000 point signup bonus (35,000 points if referred, so let me know and I'll refer you). You get 10,000 points after your first purchase, and the rest of the points after $5000 spend in six months (easy to do even if you do not spend a lot, using the tricks I mentioned). Now, these points transfer to LAN at a 1:2 ratio (with a 5000 point bonus) which would give you 80,000 LAN miles. This is enough for a coach ticket to Miami. There's lots of other deals out there too...
