Take a look at StatusNet. That's effectively a Open Source Twitter Clone.
I think non-profit and open-source might be being confused here. I'm talking about a highly publicized non profit utility style global API. To make it easy build-on and fast to proliferate it should probably be an always-on centralized service.
OStatus.
Kind of but not Wordpress as Wordpress is far too bloated for 140 char status's. I'd relate it more to Diaspora that Wordpress personally.