Personally, I’m far more interested in political parties’ policies than the socio-economic characteristics of the elected or appointed politicians. For example, in the UK a clear majority of the cabinet ministers are from upper middle class backgrounds and attended Oxbridge universities, so they have little in common with me, but I’d rather have, say, a Conservative government implementing more of the policies I agree with than a Labour government, even if marginally more of Labour’s politicians come from a similar background to myself than Conservative politicians do.
So, while ethnic minorities might prefer more appointed ethnic minority members of the Obama administration, it’s not going to have much bearing on their voting preferences.