If a vehicle is blocking your private driveway, you can most definitely dial 9-1-1. The police will be dispatched and write a citation. You should also note that it is illegal for you, the homeowner, to block your own private driveway.
What about people with a driveway next to their home (a twin). We have a neighbor who not only makes sure no one parks in the driveway (which is acceptable), but he also painted the street so that no one can park about ten feet near it on both sides. I don't even know if his "driveway" is legal. Is there a city rule for how many feet for these things?