I was reading The Watchmen (a graphic novel) and stumbled across this expression in a conversation between two cops talking about Rorschach. I suppose it means "We'll have to put up a fight", but I am not sure.
A more common idiom is being knee deep or up to your knees in something, meaning that something reaches one's knees. When you are up to your knees in water, you have gone in to a point that you are definitely wet, and more importantly, there is so much water around, that walking gets more difficult (you move from walking to wading).
It is applied to other things as well, meaning that you are surrounded by a large amount of it, literally or figuratively (knee deep in sh!t means you are in a bunch of trouble).
In the same way, the person who said We'll be up to our butts in corpses means that once they are done with what they are going to do, corpses will be piled up around them up to the level of their behinds. Whether that will be literally the case is not relevant: the message is that there will be a fair amount of dead people, once they are done.
Note that the sentence as you quoted it is ungrammatical. It may be a typo on your side or an oversight of the editor, but it should either be we'll be up to our butts in corpses, or I'll be up to my but in corpses. It escapes me why one person would refer to multiple butts in this way.