A picture of a man with a gun at his hip accompanies an article about guns at the State Capitol, "Capitol debate triggers show of weapons", Jim Ragsdale, Star Tribune, 2013-08-20. The bearer of the gun said he feels safer with his own weapon.
His first assumption is that he is under threat of bodily harm by somebody. Are any of the state representatives or senators going to threaten him with a gun? Do any of these politicians carry a gun in the State Capitol? Maybe he is afraid Capitol security might throw him out.
His second assumption is that if he is threatened by someone with a gun that he can pull out his gun, take off the safety, aim, disable the other person before that person even fires a shot, and not hit any bystanders. Even police with extensive firearms training can't accomplish that very often. Think of the Fort Hood shooting where a police officer with a marksmanship award was downed before she could hit the shooter.
His third assumption is that nobody will sneak up behind him and grab his weapon. Many police officers have been killed with their own weapons.
His fourth assumption is that he is a "law-abiding" citizen with a permit to carry and therefore should be trusted to use his gun responsibly. "Law-abiding" citizens with permits to carry have deliberately killed others with their guns. The fired employee who killed the father of another hearing witness was such a "law abiding" citizen.
By contrast, Federal law prohibits guns in Federal facilities. The penalty for having "a firearm or other dangerous weapon" in a Federal facility is a fine or up to one year in prison or both. If the Federal facility is a court the prison term can be up to two years. See "18 USC § 930 - Possession of firearms and dangerous weapons in Federal facilities".
Interestingly, the Texas Legislature considers tampons more dangerous than guns. Its guards "confiscated tampons as possible threats to lawmakers’ safety" but waved those with guns through, "Guns at the Capitol? Beware of the recoil", Dennis Anderson, Star Tribune, 2013-08-23.