People generally don't pay too much attention to Congress. Those that would be outraged would never vote for our side anyway.
They'll pay attention in congressional races. They'll focus on the most vulnerable Republican members in swing districts, and hammer them on this.
Republicans did the same thing with Nancy Pelosi in Congressional races because she was unpopular, and presumably they had some data showing it was effective. It's not like it's going to result in a hundred seat swing, but if it affects 5 to 10 races, that's a lot.