Absolutely would vote no, as I've said repeatedly elsewhere on this board.
It is no more constitutional to bar those on the terror watch list from purchasing a firearm because some may use them to do harm, than it is to deny those on it from visiting a place of worship because some may be inspired to do harm in them. The United States should not be able to permanently, or quasi-permanently, violation a citizens constitutionally protected rights without due process.
If you want to do something with the Terror Watch List as it relates to guns, there's a simple and reasonable solution. When a background check is ran for a gun purchase, the name is checked against the Terror Watch list. If it comes up with a match, it sets off a flag at the Terrorist Screening Center. Once flagged, it is reviewed by analysts in conjunction with any and all other information they have on the individual to make a determination on how relevant of an issue it is, just as they do with other actions that may bring about suspicion to those on the list.
This would allow us to at least be aware of when these individuals are becoming armed in at least ONE fashion, it would allow the government to potentially better track the flow of these weapons if they're being purchased to flow elsewhere. It also wouldn't set off a giant red flag alerting the person that they may be on the terror watch list if they go to a store and have their purchased declined despite not filling any of the other criteria.
At the same time, it does not restrict the rights of innocent civilians who may be wrongfully placed on that list, and truly everyone on it who are not actually automatically a part of an on going investigation let alone actually convicted of any crime.
What would be rather funny is that if such a law passed, in order to be consistent, the ACLU would be one of the biggest opponents of it as they (like seemingly many liberals until now) were large critics of things like the Terror and No Fly lists, questioning their constitutionality and complaining about them being used as justification for far less pervasive and continual negative actions (such as more security at the airport).