Some Congresspeople have made ill-advised claims around Assange, but to my knowledge he is not tagged as an enemy combatant in a war on terror and there would be quite a lot of surprise if the US sent in a SEAL team to shoot him.

Just clarifying, because there's a history of state-sanctioned assassination attempts and plots during the Cold War.

There should be nothing remotely controversial about these events existing.

Second, by asking a clarifying question I am not implying that the "US is not currently in the business of assassinating high-visibility targets" because I have no way of knowing this. I just want to clarify this person's point-of-view.

Of course there would be a lot of surprise, that would be an open act of war. The US's preferred method would be a drone strike operated from within the US borders, just as Russia's preferred method is with some radioactive poison.