There are several divisive strategies that the University (read : the Man, the Bosses, what-have-you) has to break the TA union’s efforts to get a contract negotiated. The first is to convince the undergrads to blame the TAs. In a normal strike, many customers will not cross the picket line because they can go to another business. This doesn’t fly in the university setting — students (or their parents) are paying big bucks, and the university can punish undergrads by telling them that their coursework won’t count for this semester if the strike continues. The undergrads will turn around and blame the TAs, lending support for the university’s position.
A second problem is institutional. Graduate students in the sciences and engineering are most often supported by research assistantships for the bulk of their time. TA-ing is considered an obligation for graduation or as a means of support when grant money is thin or you are working on your dissertation. Graduate students in those fields are sometimes ambivalent about the union, because “it doesn’t really affect them.” The GSI (read: TA) union at Berkeley is pretty strong, despite the off-putting sloganeering and obligatory “in solidarity” at the end of every email. I’m very pro-labor, but they use rhetoric that was in vogue back when the Wobblies were news. I know a lot of people who did not join the union simply because they didn’t see the point. The workload for TA-ing varies widely across departments — richer ones hire separate graders, for example. By encouraging this heterogeneity, the inclination to authorize or participate in a strike is reduced.
Finally, the university will invariably give a misleading characterization of the benefits offered to graduate students. Since their whole position is that TAs are students first and employees last, they lump in tuition, fees, and all other benefits as the total compensation given to graduate students. These figures show the truth of the situation — without paying TAs, they wouldn’t get the tuition money anyway and they’d have to hire adjunct faculty who are on average more expensive. But by just trotting out the figures they can make it seem like grad students are handsomely compensated for their time. Again, these figures are for the consumption of undergrads and parents — my tuition is much less since I’m in-state at a public school, and wouldn’t look quite as impressive.
Anyway, more power to the union, and I hope the university comes around.