I just read this post and both jimster and admin are, in part, right.
I needed to call a 1-866-xxx-xxx number in the US while in Mexico.
I tried the combinations mentioned above, but the only one that worked was 001-883-xxx-xxxx . This was from a Telmex land line (not sure if this changes if you use a different company). I also got the female voice letting me know this would not be a free call, but I had to add the international code to dial (001).
Thank you very much, jimster, for your information! I had no clue we had to change the “area code” part of the number in order to connect 🙂