Maybe they were just opposed to another government entitlement program?
The extra 430mil, IIRC, was a union figure. I'm not sure what the real figure was. Further, the 'do no harm' fund for vouchers was only created for 5 years (with 'surplus' tax money), thereafter, the $3000 would be taken from the school budget with the remaining $4000 retained by the school (with one less student).
In terms of taxes, vouchers, of themselves, should not have increased taxes as in 5 yrs the money would be pulled directly from ed budgets (as noted above). Where the increase come in is that we will have about 150k more students. If some of those went to private schools, it would have saved taxpayers money as there would be fewer public buildings to build and teachers to hire etc (private schools would increase teacher hiring). Unless you actually believe that the public ed monopoly wouldn't just ask (demand) for more $$$ and look for greater efficiency and innovation.