FYI, got this back from my Basecamp ticket:

Right now it isn't possible to create to-dos in Basecamp that automatically recur. The best I can suggest would be to use a To-do template to make re-creating similar to-dos lists much easier. Here's how: http://help.37signals.com/basecamp/q...se-to-do-lists

Hopefully that will help until we can add this feature. It's a request we hear from time to time and I hope that we'll be able to add it in a future update. We'll definitely keep your suggestion in mind when the time comes.