Is it constitutional to have a separate law covering threats against the U.S. president?
Yes. In Watts v. United States (1969,) the U.S. Supreme Court noted that “the statute under which petitioner was convicted (18 U. S. C. S. ยง 871) is constitutional on its face. The Nation undoubtedly has a valid, even an overwhelming, interest in protecting the safety of its Chief Executive and in allowing him to perform his duties without interference from threats of physical violence.