The first time one of those private companies blows up a rocket and kills a crew of astronauts, the resulting public outcry will put NASA back in the astronaut-launching business instantly.
And if that doesn't turn out to happen, so much the better.
It's possible Obama is calculating enough to see this.
Accidents happen. You can't calculate for accidents. Currently Space exploration are very centralized around government's willingness and ability to invest on it. For long terms sustainability and for space program to really expand we need more than a few players.
We need heavy investment from private sectors. This will happen eventually, why wait?
And if that doesn't turn out to happen, so much the better.
It's possible Obama is calculating enough to see this.