I would assume that it means the governor has 15 days from the time a feeding tube has been ordered withdrawn to have it reinserted.
The law is covering more people than Terri. Since it states that a relative must be protesting the removal, I assume that the order to remove a feeding tube will likely come from a court. I guess they want to avoid a last minute reinsertion, keeping alive a person who has already been severely damaged by no nutrition.
The bill appears to be a one-time use law. That is, he has 15 days to use it on one person. Then it expires (though the stay will remain in effect).