I'm not a lawyer and don't have a copy of your lease, but if you leave owing money, they probably still could come after you.
If you pay within the 3 days, then (unless your lease provides otherwise) you can stay.
If you don't pay within the 3 days and you don't leave, your landlord probably will go to the sheriff's office to have you physically evicted.
For further clarification, see a lawyer.
Hope that helps.