All it would take is 3 strong teams, which CA, TX, NY and a few others are capable of fielding.

CA already provides one third of the US olympic team, and would rank 4th or 5th if competing as a single team.
This might give the US 3 medals in Basketball instead of 1, but this still would be 1 Gold at best and therefore not impact the overall ranking much.
On another hand, how many athletics and swimming relay gold medals would you kiss bye bye? Probably enough for China to pass you over.
In Athens, the US gathered around 100 medals for more than 500 participants. If anyone, wherever in the US, would have had more chances to get a medal than the 400 US athletes who failed to get one, they would have been selected.