For the most part airlines, when they cancel flights, will reschedule you on the next available flight for which there are seats available. Meaning that if the next flight going out is already full with passengers, already ticketed and scheduled to depart on that specific date, then you would have to wait until something opens up.
My in-laws were stuck in St. Martin an extra 3 days last year due to snowstorms in the northeast US last year. The next available seats were not until mid-week and they ended up flying back to an alternate airport (PHL instead of EWR). That was the soonest that Continental was able to accommodate them. All prior flights were booked solid.
We had something similar flying Delta at Thanksgiving. Our flight to EWR was cancelled. We were given the option of flying standby on the flight one hour later or being scheduled with seats available on a flight later that evening or as we opted, we flew instead into PHL an hour after our originally scheduled departure. Transportation from PHL to EWR was our responsibility.