As Ryan T alludes to, in the American peacetime army there seems to have been a preference for deploying in two ranks, but James Walker's paintings clearly show US troops deployed three ranks deep during the Mexican War. Walker accompanied Scott's army, so its possible that this was unique to Scott's army and Taylor's army didn't use 3 ranks.
Here is an article with two of Walker's paintings showing three rank formations:
link
Winfield Scott produced multiple manuals, but the 1835 manual is considerably different from his earlier manual (often reported as 1830, but it appears to originate in the 1820s). In many ways the 1835 manual is much simplified, although more complete.
The Mexican manual that I've seen is dated 1830 and it was for militia. It only had two ranks. Interestingly this manual shared some passages with a contemporary manual by Scott (which likewise also only has two ranks).
Scott's 1835 tactics was basically a copy of the French Ordonnance of 1831. I suspect the Mexican Army probably copied the same French manual, but I don't know for certain. Assuming they did, they too could deploy in either three or two ranks.
Like Ryan said, they deployed "elbow to elbow" in both armies. I don't know where the "four feet" per man frontage comes from. It is very excessive for close formation, too close for skirmish, and doesn't fit any formation in any manual I've drilled in*. In fairness, I know of few people who actually base their miniatures so that they are jammed together in elbow-to-elbow formation. :-)
*OK -- it's kind of close to the late 16th century pike drill I've done, but that doesn't seem to be applicable here. ;-)
