Okay, from the page of the main bus terminal in Buenos Aires (Terminal de Omnibus de Retiro - Retiro Bus Terminal), The destinatinations that are at least 30 hours away (according to google maps) are:
Argentina
*El Calafate, Santa Cruz - 34 or 36 hours
*Río Gallegos, Santa Cruz - 33 or 34 hours
*Rio Turbio, Santa Cruz - 35 hours
also from Río Gallegos you can reach Ushuaia, Rio Negro, Puerto Natales and Punta Arenas.
And many latin american destinations which are more than 40 hours away by bus, but i think they are starting in Argentina, because if they were starting in another country the would have been transported by plane, rather than a 36 hours journey by bus. I also think, that the starting point is a place with no airport or a little one, or the we have a low budget this season.
So i would go with a Patagonian starting point, I would say Santa Cruz or Tierra del Fuego Province in Argentina, or Aysen or Magallanes Region in Chile.