First, I readily admit that I might be completely off on my intrepretation of the rules, but according to Brett McMurphy's article on the subject (
http://espn.go.com/college-sports/story/_/id/8742607/seven-catholic-schools-leaning-leaving-big-east-sources-say) ..., well, let me go through my rational step by step:
(1) It takes a 2/3 majority vote to dissolve the Big East
(2) Due to the teams leaving and joining the league, there are only 10 members eligible to vote on disolving the conference (the 7 Catholic schools + Cincinnati, UCONN, and USF...Temple does NOT get a vote because its not yet a full member), meaning that the 7 Catholic NON-FBS schools have the votes to dissolve the league
(3) McMurphy states "If the seven schools decide to move to a new league, they would keep their automatic berth in the NCAA tournament. NCAA rules state that as long as a group of seven universities have been in the same league for five years, they would keep their bid after a move together."
Leaving aside what happens with the name or previously earned NCAA tournament monies, I think this means that the 7 BB-only schools could vote to dissolve the league and "instantly" reform it around themselves, with or without the addition of varied other members (e.g. Dayton, Xavier, Butler, etc) without worry of losing their conference's NCAA-autobid.
If I read the rule correctly, it also means that the remaining schools (or Big East Refugees as CMoney named them) would NOT immediately have an automatic NCAA-tournament spot were they to try to form a standalone league: among the current-future Big East membership, there is no combination of 7 schools that have been in the same conference as one-another for 5 years.