The exempt entry (entering the kingdom without a visa) is only 30 days. With your travel dates you might end up on overstay by 1 or 2 days depending on when you arrive in Thailand. Recommend you purchase a single entry tourist visa from the consulate in America which will get you a 60 day stamp when you arrive.
I'd be very leery of heading to Mae Sai on an overstay. We've seen posts with other people on their way to do an out/in bounce with overstay and got pulled off the bus by police when they checked their visas. Even caught on one day overstay can land you in jail or get you kicked out of the Kingdom. Assuming you're coming from Chiang Mai or Chiang Rai, you will go through several police check points. Why take the risk?!
If the actual visa expires Jan 8 you could do a quick border run before your trip to get you another 60 day stamp. Then you can get a re-entry permit to keep that 60 day stamp alive. You can then extend that 60 day stamp by 30 days at local immigration as well. But, it really depends how long you'll be staying in Thailand.
Chiang Mai it's free.... but takes a month. If you want 1 day turnaround they direct you to the agent across the street for 1000 baht. Tipping by proxy ;).