strictly speaking according to law, you need the original with you. Yes, I also carry a copy, but I know someday I will come across an overeager cop looking for tea-money
, then still passport needed, law says Thai citizens must have their ID card on them at all times and foreigners must have their passports on them at all times
Never a good idea to have an overstay stamp in your passport, can make entry into other countries difficult. I would be very worried about being asked by Police for your passport in those 2 overstay days, then it is off to a Thai jail, and a 5 year ban