Meet with the board and discuss with them likely outcome if this problem is not addressed in a timely and appropriate way.
Make sure the problem was not created by your staff. A staff member’s failure to plan ahead or respond correctly should not become an emergency for the board. If it was created by your staff, apologize to the board and promise it won’t happen again. And then advise your staff that any other such egregious errors will not be tolerated.
Sell the problem, not the solution!
Never internalize the problem or get locked in on a single solution. Remember, it is their kids, their school, and their money. They have a right to make a decision that you consider to be wrong. Your job is to be the dispassionate "doctor" in the room and help them understand their options and the consequences (positive and negative) of each option.
If the board asks you for your recommendation give them options (plural!) with the consequences of each option. But wait until they ask. There is a "readiness factor" in decision-making and you shouldn't make the mistake of pushing for a solution before they are ready to make it.
The larger or more controversial or more difficult the problem, the larger and more diverse the number of people who should be involved in the solution. Special care should be taken to involve people of divergent opinions.
Go slow! The more rapidly you are able to conceptualize a problem and the options for solving it, the more patient you have to be for others (the board or your staff) to catch up.