The Brady Campaign, in addition to several other gun control advocacy groups, including Mayors Against Illegal guns, have latched on to this new "Terror Gap" issue, which advocates using the federal government's "no fly" list to deny gun purchases for American citizens. No one wants terrorists getting a hold of guns and other dangerous objects, but in the battle against terrorism, we should be careful not to surrender our rights and liberties, including our Second Amendment right to purchase a firearm for self-defense or recreation.
Currently federal law prohibits people convicted of certain crimes, or who have been adjudicated mentally defective, from purchasing or possessing a firearms. But a key aspect with either of these two situations is that the prohibition is not applied until the person has been convicted or adjudicated through due process of law. There are no such protections against getting added to the list, and no defined process for getting oneself removed. There have been a number of prominent individuals who have found their way onto the terror watch list, usually because they share a name with a terror suspect or his alias. Famous people who have ended up on the list are Composer John Williams, the late Senator Kennedy, and dead guitarist Robert Johnson, along with anyone unfortunate enough to share their names. Numerous problems with the no-fly list are probably why even liberal groups like the American Civil Liberties Union believe the list is unconstitutional.
There might be some disagreement and difference of opinion about exactly what our Second Amendment rights mean, but one would hope that most Americans would agree that no right explicitly protected by our Constitution can be removed or abridged in the manner the Brady Campaign suggests. We can be pretty sure that when our founders wrote "shall not be infringed" into the Bill of Rights, they didn't mean subject to cancellation at the whim of an unelected government bureaucrat with a list.