First Ammendment not withstanding, there are a number of laws on the books that regard the mere act of threatening verbally or otherwise as a punishable crime. In these cases, the threat itself is recognized to carry potentially serious consequences if ignored. Thus, merely making the threat is considered a crime. Once a year, for every one of my 20 years in the Air Force, I recieved training titled "Protection of the President" (note, that would predate our currently sitting president). If I were in that bar and heard the statements this person was purported to have made, especially in light of the fact the Prez would be in the area, I would have no choice but to take it seriously and report it. As pointed out, this is not the first time someone has been arrested and convicted for making threats against a President of the United States.
Another thing I was taught in the Air Force (and before that by my father) was that I would show respect for the Office of the President, regardless of who it was that sits there. That doesn't mean I can't publically disagree with his policies (unless I was tasked with carrying out said policy), but I was to do it in a repectful and civil matter.
In an interesting asside, it was former President Clinton who actually created changes in the Uniform Code of Military Justice (UCMJ), making it a punishable offense (for those in the military) to publically ridicule or otherwise poke fun at the President. Read what you want into that.