Jonathan Bernstein insists that Haley Barbour actually did run for president:
[W]e call this period the "invisible primary" for a reason: just like in the state-by-state primaries to come next year, the current contest has winners and losers, and the losers tend to drop out. Now, some potential candidates really haven't contested the invisible primary…I haven't read anything, for example, about Jeb Bush. So I'll chalk him up as a "did not run." But those who hired staff, sought endorsements, traveled to Iowa and New Hampshire and South Carolina — they contested the invisible primary. They were candidates for 2012. Even if they didn't quite make it all the way to 2012.
The Dish 