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Basically, there are twice as many eligible workers in the economy now, and so labor groups lost lots of bargaining power.
I don't necessarily buy this explanation - but there have been some somewhat serious efforts to quantify this effect when looking at wage stagnation.
The mistake wasn't bringing women into the workforce, it was doing so on terms that nakedly favored capital and screwed labor, men and women alike. We should probably revisit those at some point.
I don't think its a very interesting hypothesis though. The increase was fairly gradual post-WWII [1]. It also seems like it probably points the causal arrow in the wrong direction. Women probably would not have entered the workforce in such broad numbers had economic conditions supported a single income earner per household.