The problem in Giffords' article is not the use of emotion, but, rather, the overuse of emotion. The three modes of persuasion are ethos, pathos, and logos. Pathos, the use of emotion to persuade, is most effective when used with logos (logic) and ethos (credibility of the speaker). She employs some ethos by referring to her terms in Congress. Much or all of that is lost by the over-emotional name calling (calling them cowards, etc.). This is a turn-off for most readers and listeners. She employs absolutely no logos.
When we make our arguments, we should keep these modes of persuasion in mind. Try to craft your arguments with some facts -- "Here's some things they're not telling you about the bill," or "Did you know Internet sales already have to go through a FFL?". Make a calculated but respectable plea to emotion -- "Patriots beginning with the battles of Lexington and Concord have fought and died protecting our Constitutional right to keep and bear arms." Unless you are a publicly known and respected figure, you have to build ethos through the respectful, yet forceful arguments you make. We won't persuade the hard core opposition but we may be able to hold the middle.