"It depends."
Not the answer you want to hear- but true. If you get a 1077 that, from the factory, will shoot reasonably close to the 625fps maximum output you can kill squirrels at 20'.
If you get one that wasn't quite 'up to spec' that left the factory- which seems to be all-too-common on 1077s, you may not be able to kill anything effectively (some guns have been seen as low as 350fps from the factory).
You can get one, try it, and if no good return it and see if the next one is better. Or, you could get a 700fps-range springer- i.e. like a Crosman 795 as an example.
Whatever you use, use 'hunting' or pointed style pellets, or maybe hollow points- but don't try killing anything with 'wadcutter' (target) pellets.
http://www.airgunhome.com/agforum