The typical argument is usually about the .223/5.56 calibre, with a 50/50 split saying it's enough with good shot placement, and others saying it's still not enough (preferring 308/30-06)
According to ballistics101.com, a 357 mag is getting a muzzle velocity of 1300-1600fps, with ft/lbs energy in the 500-800 range.
.223/5.56 on the other hand is getting 2800-3200fps, with energy ratings of 1000-1500.
Granted it's a bit apples to oranges because a 357 is a larger bullet moving slowly, and a 223 is a smaller bullet moving faster, but the 223 still has twice the energy. Not only that, though, but higher velocities make for a flatter trajectory and a higher probability that you'll hit what you want from greater distances.
Could a 357 kill a deer? Absolutely, and some people will swear that all you need is a 22LR. However, if there are debates about the 223 and whether it's enough, a round that only has half that much energy is what you're asking about.
That said, if you're a fan of handgun calibre levers for hunting, why not step up to a 44mag? I've got a Winchester 1894 trapper in 44mag, and I'd feel much more comfortable shooting a deer with it than with a 357.