The US does not have "absolute freedom of speech". Try sending a believable death threat to a federal politician on twitter (don't, the secret service will track you down and arrest you- it happens more than you think)
However, the act of threatening someone is punishable, and it does not matter whether they are a politician or an ordinary person. What matters is that you committed the act of threatening to kill someone, and that is a crime regardless of the medium or act through which the threat is conveyed.
You can, ie, argue how death penalties should be applied to politicians who violate a certain rule.
You cannot and should not be able to threaten one specific individual. If anything, we need more of that kind of enforcement. So many deaths could be prevented if only all jurisdictions handled this matter as seriously as the Secret Service does.
EDIT: wording