The time it takes for the police to get a warrant depends on how severe the case is for getting the warrant.
If it's a warrant they need as soon as possible the police can get the warrant issued to them within 4 to 5 hours but for some warrants I've known it to take a week or even a month to get the warrant to the police so they can serve the warrant or enter a home with the warrant.
It all depends but in most cases the warrant usually gets to the police within the same day if they need the warrant that badly.