I just discovered the tube of Polysporin I dropped, in the attic.
And clearly a mouse or mice had found it yummy and eaten the entire medium sized tube, which was nearly full!
So, if it was one or two mice, will it kill them?
(As soon as I discovered it, I set about laying a couple of traps. Then I got to wondering if I need bother!)
Yikes! Or did you just create a strain of super-antibiotic mice??
It might make them healthier.
I doubt it. It’s some kind of petroleum jelly base with antibiotics in it, right?
If that’s what it is, I would expect that the mouse would not be able to digest the jelly, and it would just pass harmlessly out the other end. If you found the poop left by this mouse, it would probably be greasy looking.
And yeah, the small amount of antibiotic absorbed might just make it healthier.
The only way it would be harmful is that there are some drugs and some food substances that are harmless to humans but hurt animals. However, most pharmaceutical drugs are tested on mice heavily…
Yea, but not everything made for topical application is meant to be eaten. 
If Polysporin is based in part from bacitracin, it appears that it is toxic if used internally (which could mean ingested). Depending on the dosage the mice got, it could give them some kidney failure, eventually.
Another thing to consider, depending on the combination, is what is the spectrum of bacteria affected. If it is mostly gram-positives, then the mice may end up with bad bacterial overgrowh in the intestines and a really bad enteritis that can kill them.
So the answer is… possibly, but not necessarily and not perhaps as quick as you want.
Mice will eat the weirdest things, won’t they?