So far, each union local to vote has trumped the last in both turn-out and support for strike authorization. The latest is GAU, which had a 88% voter turnout (late on a Friday afternoon) and a 97% yes vote. Kristi Brownfield, a GAU stalwart who deserves much of the credit for this vote, reports the details on Unions United. They also signed up 54 new members on Friday alone. I don't have total numbers for GAU membership (and will go ahead and agree that the unions ought to be less coy about this), but 54 new members in one day shows that there's considerable upside potential there.
I don't know about you, but I think that authorizing a strike takes a good deal of guts if you are a GA. GAs obviously depend on their stipends to put food on the table. And while the rest of us may have been in Southern Illinois long enough to develop networks of friends and family to help support us should we need to miss a paycheck, most GAs will not have done so.
The Southern prints numbers given to them by the administration, which counted all of 77 dues-paying members in July, but that number has obviously risen. There are obvious hurdles to getting GAs to join, among them the fact that a big chunk of the something like 1750 GAs on campus each year are new to the job. The local has only just received contact information for new GAs. Many GAs are just learning that they are represented by a union--this isn't information the university deigns to share with them at orientation, from what I understand.
Plus you've got to face the fact that at least some of your professors aren't union friendly; that the chair who is your ultimate boss is classified as an administrator, and hence part of the team that is supposed to be working to plan how to negate the effect of a strike (though of course many chairs are sympathetic to the union cause), etc. Dues aren't extravagantly high, but you're trying to live on a very low stipend every dollar counts (and your earnings so far this semester haven't yet amounted to a year's worth in fees). The pressure to just sit on the sidelines and not join is tremendous.
Would the unions be stronger with more dues-paying members? Yes. So you can argue that lower membership makes them weak. But relatively low membership is largely a result of the way Illinois law works--allowing for people to elect to form a union and then elect not to join, to support a union with their vote to certify it but not to put their money where there vote is. And at least as important in judging the unions' strength is the trend in membership. If faculty, civil service, and GAs were indeed turning on their unions, we'd be seeing declining numbers. The fact that more are joining now--precisely when becoming a union member is generally going to mean that you are saying you are prepared to go on strike if it comes to that--is pretty powerful evidence, to my mind, that support for the unions on campus is growing.