The electric company can disconnect your electricity at any time they want too but most will not disconnect your service right away after being pas due.
With most electric companies your electric bill will have to be at least 2 months behind before they'll disconnect your service and they should try and phone your or contact you at home before you'll be disconnected.
They should also send you a disconnect notice to give you time to make payment arrangements or pay the bill in full.
If you're behind on your electric bill phone the electric company up and setup payment arrangements with them.
In the winter time they're forbidden from disconnecting your electric service from November 1st to March 31st in most places and in some places if it's above 95 F they cannot shut off your service.