re: Which programs
The federalization of education, as with the federalization of many other things, was largely a Democratic goal. Note I say "was." Republicans seem to be enthusiastic about this kind of thing too, now.
If you need proof that most of our large-scale Federal and state social programs have "Democrat" written all over them, then I don't know where else to go with that one.
Democrats for many years have taken credit for pretty much the entire "Great Society," never mind the "New Deal." They should be able to deal with the actual results, too, not all of which have been positive by any means.