Assuming that the US Government is interested in playing fair.
Prove it
I'm guilty here of presenting an argument from incredulity but I prefer to think o fit as applying Occam's razor.
The US government has a much better relationship with the UK than it does with Sweden (after all the UK was its lapdog and have supported all of its Middle Eastern adventures) and the UK/US extradition treaty is so asymmetrical that it is ridiculously easy for the US to obtain extraditions fro the UK without even having to disclose the evidence to support the accusations. So here comes the argument from incredulity....
If you were the US and you wanted to extradite someone so that you could prosecute them for releasing secret materials would you......
Bring charges that you actually want to bring and then attempt to extradite that person from a country who has backed you all the way on Iraq and with whom you have a extradition treaty and who have demonstrated their willingness to co-operate with extraditions and in particular with security based extraditions.
OR
Get another country with whom you have a much more prickly relationship and who have a judiciary which has hitherto demonstrated that it will not bow to political pressure to bring false unrelated charges of a sexual nature which will allow that country to extradite Julian Assange from the UK and then you can extradite him from Sweden.