All I know is that I appreciate that we do not have the diversity of varmints in the UK as the USA!
I do know that the terriers we have would have a go at anything that is remotely smelly and wild if not told to leave it.
A mink was trapped on the fishing lakes and my Border Terrier knew better than to touch anything in a cage. However she was curious to what this smelly creature was and put her nose to the trap.
The mink bit her through the lip and nose. Never before have I seen a dogs eyes turn scarlet. The biggest bit of the mink would have covered your thumb nail and the trap was annihilated.
It is unlikely to be mice, you would small them and they will only carry off a little food and nibble at the rest. You would find a lot of crumbs.