Romney's comment that he likes to fire people was probably his biggest mistake, as more voters have reason to fear being fired than are in a position to fire others.
This will rank with Tom Dewey's "He should be shot at sunrise" remark.
If Donald Trump had said that, it would not have hurt him in the least bit. And it, on its own, did not hurt Romney in the least bit, either. It's Romney's broader message that sucked for the rust belt, and Trump's message that won him it. See
The Gamble: Choice and Chance in the 2012 Presidential Election for more evidence on the long-term lack of effect of gaffes.