Less Chumras
You are correct that for the 2015 term they won enough seats to control the senate but just barely. They won 32 out of 63 seats and currently have 31 seats so they need the Democrats. Even with the one vote majority it’s hard to pass anything without Democratic support. The Democrats are controlled by the unions who are against any support for non-public education, that is basically what is blocking it.
Once the government starts paying for the children’s education they will want to micro managing what is taught and how much is taught. This is already happening in regards to pre-k. We don’t need it. A better solution is to grant tax credits for education. The parent or relative will get a tax credit on their income tax for tuition payments. The taxpayer will be subsidizing yeshiva education indirectly and not have the power to micro manage the yeshivas, just like than any other tax credit program.