Just to play devil's advocate here: How are Sweden supposed to promise not to extradite him to the US? Wouldn't that depend on what kind of possible extradition request would arrive, if any?
http://en.wikipedia.org/wiki/File:United_States_extradition_...
It may be that the US could give undertakings about excluding punishments (such as death) to the Swedish government that would make an extradition possible. As far as I know, though, Assange cannot be tried with treason in the US (which has a possible death penalty) because he is not a US citizen.
[1] http://en.wikipedia.org/wiki/European_Convention_on_Human_Ri...
http://europa.eu/legislation_summaries/justice_freedom_secur...
Why someone would flee Sweden to go to the UK when they are afraid of US extradition is beyond me. The UK has a much closer relationship with the US.