In August 2010, Twitter switched 3rd party login protocols from "Basic Auth" to "OAuth." In a nutshell, this is a more secure remote login system. What does this mean for you and your Twitter client?
NatsuLion has been removed from this list. NatsuLion doesn't support OAuth. When I checked the NatsuLion page recently, it looked like it hadn't been updated in over year. At this point, I'd consider NatsuLion to be simply non-functioning as it's no longer under development and will not interface with Twitter.
All of the clients listed here have been updated to support OAuth. If you haven't updated yet, you won't be able to log in to Twitter at all from your client. Simply follow the link to your client in this article and update.
If you're still using Tiger (10.4), consider Buzzbird, an open-source Twitter client that is basically the bizarro Twitterrific, only with more features and no ads. I've been using Buzzbird for months and find it an excellent client, and it replaces NatsuLion as our fourth OS X Twitter app in this list.