These are the latest youth cohort party ID numbers from Pew. As you can see here, the future looks a bit bleak for the GOP. The chart illustrates the fact that, contrary to myth, the Democratic edge with young people has usually been pretty small but now it's huge. In a micro-sense, of course, anyone whose experience consists mostly of eight years of peace and prosperity under Bill Clinton followed by Bush acceding to the White House under dubious circumstances and then leading us into inept governance, failed wars, and a shaky economy is bound to favor the Democrats.
But in a macro sense, you're looking at the undertow of the past thirty years of conservative identity politics. The right has had great electoral success mobilizing people against the kind of social transformation we've been experiencing for the past several decades (more and more assertive racial and ethnic minorities, secularists, cosmopolitan types, etc.) but they haven't actually halted any of these transformations and the lines of cleavage that have given the GOP the bigger half of the cookie in most elections since 1968 leave them with the smaller half among the youngest cohort.