People are only looking at a twitter widget to catch tweets though. If your design is any good, and it seems it must be, then the widget is clearly shown as listing tweets (I can't think what else it would do). Getting people to notice the widget and not then discard it as "just twitter" or use it as twitter and follow the line the tweets send them on seems like too much of an ask IMO.
Adding back links to affiliate pages and selling something using your promoted position in the SERPs seems the most probably model to me, just unfortunately quite scuzzy too.