If you contact the Progressive Insurance agent by phone to cancel the insurance with Progressive then it should be canceled immediately but if you do the cancellation of the progressive insurance online then it might take an few days for the insurance policy to be canceled.
If you're canceling an auto insurance policy with progressive you need to make sure you already have auto insurance through another company before driving your vehicle.
Otherwise if you get stopped or into a car accident then you could be into some serious trouble.
Be aware that in some states Progressive may charge you a cancellation fee to cancel your auto insurance policy with them before your policy runs out.