In things such as statistics, probability, economics, and social psychology "common sense" is typically misguided. That's why people who wish to treat these fields as SCIENCES must seek evidence.
I agree that the second was better that the first, and that the first was less-than-perfect. But I can't imagine one person who would actually take time to learn the liberty message who would be so off-put by a "soundbyte". That's not to say that they don't exist, but the comments to the Daily Caller article show people who already hated Paul and this just reinforced their position, and those who already like Paul who, at worst, said that the message was right, but the time and form wasn't perfect. I didn't see one "I would've looked into the liberty message, but this is just too far out."
So again, where is the evidence? Show me that more people were lost than were gained. I haven't seen evidence for the numbers of either group.