American public schools have a rather big problem largely stemming from unnecessary centralization. Also, the more money they get, generally speaking, the worse of a job they do.
Besides that, it wouldn't be really fair to say just the Republicans are in demographic trouble. True, they have far fewer bases of support than the Democrats and are going to shrink if they continue the way they do, but the Democratic "coalition" is incredibly tenuous and largely dependent on the Republican party views remaining constant. Midwestern union workers, Hispanics/other minorities, women, the youth, and intellectuals really are only all on the same side because the Republicans in power right now have an uncanny tendency to alienate everyone except those with their very narrow subset of views. Obama, at least to some extent, tried to appease all of the wings of his party by not going too far in one direction (for example, pushing gun control or environmentalism as issues), and held the coalition together for the election. Romney, meanwhile, basically took the wholesale "Mainstream Republican" views on every topic and didn't even try to please the different wings or consider what was worth saying and what wasn't. He also had the Paul supporters unceremoniously chucked out of the convention and managed to alienate one of the few "independent" groups that might have ended up supporting him.