Nothing, the neoliberal media will write 100,000 articles about how she's the "princess" of the "despotic ruling family" and the libs will nod sagely along, unbothered by any troubling thoughts of cognitive dissonance the next time they get horny for a Michelle / Malia / Sasha or a Hillary / Chelsea royal flush - saving all their energy for a scowl and a magnificent "aw shucks" shrug when you ask them about the Bushes or the Kennedys.