When did Republicans cut any of those things? Schools are funded locally by the local taxpayers. It's up to the people of a community how much they wish to spend for their schools.
What lowered birth rates is the cost of raising a child today. According to the CDC, the cost to you will be $233,000 to raise that middle-class child up to the age of 18. If you want the standard 2 child family, you better be willing to cough up a half-million dollars in the next 20 years or so.
The people who have the larger families are those that mostly depend on government assistance. Working parents are limited based on their income. As far as the lowlifes are concerned, the more kids, the larger the SNAP's card, the larger the HUD home in the suburbs, the more TANF, the larger the welfare check.
By providing for those parent(s), we are creating more poor people since the apple doesn't fall far from the tree. There is no incentive outside of tax breaks for middle-class families to procreate.