So far everyone has said that the Juggernaut Maniac runs faster than normal so its possible it has build-in speed perks and possibly Extreme Conditioning, however that has not been confirmed.
At the 1:40 mark in this video the player unloads into a full-health Juggernaut Maniac with a suppressed Honeybadger. The suppressor shouldn't affect the gun's damage because it's at point blank, but I can't say that for sure.
From what I could see there was one shot that missed and the juggernaut died with the very last bullet in the magazine. The first 13-15 shots were in the head, then there were about 4 body shots, then some neck shots, the one missed shot, and back to the neck for the rest.
It seems reasonable to say that gun's damage is between 30 and 45 up close and a headshot multiplier 1.4 (standard for MW3 assault rifles), which would put the juggernaut's health between 1026 and 1575
Even if those numbers are slightly off I think it's safe to say that the Juggernaut Maniac has at least 900 and at most 1700 points of health.