I am not sure if this is true - blue collar rank and file tends to be socially conservative and patriotic and thus vote Republican. In other words, unions membership does not necessarily mean votes for Democrats - identity politics is IMHO a much bigger factor.
While we are at that, I also think that steadily declining union membership is not merely a result of sluggish organizing efforts (the standard lefty excuse). I think unions face a structural problem, which so far they profoundly failed to address. That problem is growing discord between blue collar identity politics which is still the main part of union appeal and changing nature of workforce, which is becoming more and more "white" or "pink" collar. Unions stuck the old cultural identity - male blue collar breadwinners working in "good" mfg jobs - but that cultural identity has less and less appeal to people (especially the younger crowd) working in most mainstream occupations. Yet, the unions for the most part wrote these folks off as "yuppies" and do next to nothing to attract them en masse. Instead they look for new members for whom their old blue collar cultural identity may still have some appeal.
Stated differently, for the unions to become a significant social and political power again, they need to attract a significant chunk of mainstream occupation which are increasingly white collar and professional - computer programmers, salesmen, PR specialists, doctors, educators, etc. However, the "old" union image based on blue-collar cultural identity has little appeal to these folks, and the unions did not do much to make themselves more attractive to these folks. To my knowledge, the only mainstream white collar profession that is substantially unionized is the teachers (artists or airline pilots may be unionized as well, but there are too few of them to make any impact).
And as long as it is, union membership will continue declining and unions will become more and more marginalized.
Wojtek