The number of bids changes if conf tourneys left yield unexpected results:

Unlikely examples:

ACC: Va Tech meets NC state in finals NC state wins
AT 10: Dayton meets St. Joes St. joes wins
Big East: Providence meets Notre Dame in finals ND wins
Big 10: Michigan meets Northwestern in finals Northwestern wins
Big 12: K State meets Iowa ST. Iowa St. wins
USA: Tulsa meets Houston Houston wins
Mountain: Utah meets SD st. SD st. wins
Pac 10: Arizona meets USC USC wins
SE: Auburn meets South Carolina Auburn wins

Anyone of the above or something similar creates an intriguing mess mainly because you would have bubble teams making the finals and possibly beating a good team along the way and then losing to a team that would probably not get in unless they win the tournament as shown in the examples above.
I think all of the scenarios above are possible although unlikely.
Obviously others scenarios can be created which would spawn chaos.