I am also due January 8th and I have period-like cramps sometimes also. And period-like backache. I mentioned it to my doctor at my last appt and she wasn't concerned. I'm also experiencing Braxton hicks daily. I think our bodies are just getting ready for the big day!
I am on 6th Jan, not sure if it's because this is my third baby, but I have been getting similar pains and even intense Braxton hicks as well so my thought and according to the the midwives it's my body preparing itself for that last hurdle. But if the pain is consistent and more painful make sure you contact your Dr or Labour department for help.
My due date is Jan 9th and I'm feeling those pains too. It comes and goes. I don't get them all day long or everyday so I think it's the body that is getting ready for the real contractions and labor.
You don't think it to early to be feeling this pain and my due date is Jan 8
I agree with danahenley it could be your body preparing itself, try and take it as easy as you possibly can.
I'd say its your body getting ready.