Two valid concerns were raised in the course of the Senate debate, ones which the House should be as firm in addressing, if not firmer.
First, Sen. Roy Brown, R-Billings, said that the bill would raise property taxes for many, as districts raise money for the matching funds required of districts. On a similar note, it was pointed out by Republicans that poorer districts might not be able to afford it at all, bringing inequity into the system.
Second, Dan McGee, R-Laurel, proposed that districts have the freedom to spend the money on other early education programs other than full-day kindergarten.
These are both valid concerns, and there are common-sense solutions that can be insisted on by the House -- and presented in a positive fashion, pre-empting the inevitable accusations by Democrats that Republicans hate children (which is probably why Republicans tend to have more children than Democrats -- more kids around to hate and ignore.)
Common sense solution: Make the funds outright grants to the districts, rather than matching funds. That way, every district is treated the same.
Common sense corollary: Allow districts to spend the money any way they like -- raises in teacher salaries, improvements on aging facilities, full-day kindergarten, or any program of choice that local communities think is the most acute need.
Simple. Fair. More money for every school district in the state.