The Republicans have been doing this pretty much ever since I've been in the US. The funniest occurrence was in the Clinton-Bush campaign, in 1992. The thing is, the press were well aware of what was happening, and they started to "translate". That is, when the Bush campaign accused Bill of something, they knew that was something to watch for from Bush. One simple example was a big Bush speech accusing Bill of trying to "buy" votes by promising give-aways to groups of voters (not that anyone had noticed this particularly). And the next week Bush went on a tour of mid-West farmlands, promising huge subsidies to farmers.
But the funny one was close to the election when the Bush campaign was desperate and knew they were losing. Someone accused Bill of having an affair. The press was right on it: "What? George Bush is having an affair?" "No, we said Bill Clinton is having an affair!" "Holy crap! You really think George Bush is having an affair?" "No, we said Bill Clinton!" "I can't believe George Bush is having an affair." And round and round it went for about a week. If the Daily Show had been at its peak, they would have been unbelievably funny around about then, but actually, nobody really picked it up and ran with it.