The Society has not specifically pointed to this date, but according to Raymond Franz, there are deffinately some big wigs in various branches that put stock in this date.
If the year 2034 comes and goes, the Society still has some wiggle room. Remember that Noah was given 120 years for the ark construction; but then Noah had to take time to load all of the animals into the ark.
The Society could state that after this 120 year period, that there is now a final gleaning work, where the final ingathering is taking place before the great tribulation errupts (where Jehovah decides to shut the door to his "ark-like" organization). This would see the numbers of pioneer and auxiliary pioneer applications jump dramatically.
Later on, the Society could state that Jehovah was extending mercy on the "nations" as He did with the Ninevites; and how grateful Jehovah's people should be for this extended mercy. All the while, the Society could still repeat it's same mantra that "the time remaining is short". And on and on it goes.