For blue-collar workers, single parents especially, scheduling matters-when their shifts start and end, and how much leeway they have to manage their time.
I was given the leeway to work with those funds and convince the legislature and the administration that most of that money should go into health care.
The word 'leeway' means freedom to make choices. So in this case, a person had the freedom to convince those in charge that this money should go to health care.