I just went to World Builder to test this out.
I gave myself 6 Swordmen, all with Combat I and Cover I and 3 with City Raider I as well. 2 Axemen with Combat I and Cover I joined them.
Their opponent was one Longbowman with City Garrison I, II and III on a plain hill with walls and 60% cultural border. I tossed in an Axeman, but as you'll see, it was unneccesary:
The first of 3 Swordmen with Combat I, Cover I and City Raider I attack. The odds are 0.2%! That's a 1 in 500 chance of winning! Must be the uh, walls, 60% culture defense, hills and the extra bonus associated with it for Longbowmen. After all he is a 15.9 strength! Also, let's not forget that this guy received no fortify bonus (because I didn't think about it before attacking).
Second Swordman attacks and actually does damage this time!
Third triple-promoted Swordman dies, leaving the Longbowman with 3.7 health. Now for the Swordmen and Axemen without CR to attack. I have a feeling they won't fare much better.
Just to save my upload space I'll go ahead and tell you that the city was eventually captured, however all 6 swordmen died. The first non-city raider swordman actually took on the axeman and managed to get him down to 1.5 health. This was extremely lucky as the axeman should have slaughtered him at the odds. The longbowman took out the other two swordmen before dying to the first axeman. A longbowman took out the weakened axeman, leaving me with 3 axemen and two longbowmen left. In most scenerios I think more axemen would have died before the city was taken, but considering the sheer number of troops I had compared to the opponent (6 times!) I'd have to hand the victory to the defender. One longbowman took out 5 promoted swordmen and weakened an axeman. The axeman defender put up a poor fight, but thems the breaks.
The conclusion is one longbowman is enough to wipe out an entire army if heavily promoted enough and facing a human opponent too stupid to bring cats.