I have put your sentence in a slightly less natural order, which should make it a bit easier to follow:
In an academic paper, we can't try to get away with something that we would abhor in a political debate (or worse yet, in a political advertisement).
There is something that we would abhor in a political debate. We should not use this thing in an academic paper either; for, if we would abhor it in a political debate, so our readers would abhor the same thing used in an academic paper.
The that clause modifies something; the phrase in my example sentence in italics becomes the object of get away with.
Note that we can't try to get away with sounds a bit awkward; an alternative would be we shouldn't try to get away with, or we won't get away with, or even we shouldn't expect to get away with.