In the 18th to 19th century American administrations weren't squeamish to outright use the army to gun down riots or insurrections. Influenced perhaps by the very literal "reading of the riot act" as an official threat to shoot entire crowds as an accepted thing. Attempt death threats to public officials then and the only question was if you would be shot or hanged for doing so. The appetite for that has been lost over time, perhaps related to Kent State and Tienanmen Square changing the optics from 'strong authority restoring order' to 'depraved psychopathic tyrannical government'.

Not that we need that level of violence, all that is really needed to is to give the Secret Service standard of treatment for death threats to the president handed down to all other lesser officials. If being tracked down and arrested was an absolute certainty instead of something they could think they could get away with.