This 2019 report describes which U.S cities now offer pre-K and the quality and attributes of their respective programs.   The local public finance of these early human capital investment programs has not been sufficiently studied.  Both States and cities share the financing responsibilities. 

Back in 2013,  Alan Krueger wrote (see page 188) that the most interesting issue regarding Pre-K is the political economy of "who pays for it".

In 2015, I wrote a NBER paper on the Political Economy of Pre-K.  The typical beneficiary of this program lives in the center city and is poor.  The typical taxpayer for this program lives in the suburbs and is not poor.  This physical spatial separation has implications for how the median voter evaluates this program's benefits and tax price.  Education economists have not spent enough time thinking about the urban equilibrium here.

My NBER paper.

The expansion of access to publicly provided pre-kindergarten bundles together redistribution to the poor with an early human capital investment. Financing publicly provided pre-K investment is mainly a state and local issue. Which voters favor local pre-K expansion? This paper uses several new data sets to describe the circumstances such that local voters reveal a willingness to spend on an early intervention that may not yield direct benefits for them. Republican voters consistently oppose the expansion of publicly provided pre-K. Suburban voters also tend to oppose such investment. We explore several possible explanations for these facts.