According to Fred Siegel, they’re that Republicans need to go left on social issues–because “swing voters and GOP moderates deserted them in droves” in those elections. Pretty much every group of voters aside from self-identified conservatives turned against Republicans last year. But it’s not at all clear that social issues drove the trend. I would say that the three biggest factors that hurt the GOP were 1) that we were losing a war and Republicans didn’t seem to want to acknowledge it, let alone change the policy; 2) a lot of Republicans were caught up in corruption scandals; and 3) Republicans seemed to be (and were) more interested in holding on to power than doing anything for the country–which was related to (1) and (2).
The pattern of candidate and referenda victories in 2006 does not corroborate Siegel’s thesis. (E.g., Nancy Johnson didn’t lose in Connecticut because she was too beholden to the religious Right.) Neither does the actual conduct of the campaign, in which Democrats generally played down social issues.