I bought my ticket to go back to my country according to my DS2019 dates, which expired on Dec 20 (so my grace period would be until Jan 20), but later I received another DS2019 from my sponsor with a new expiration, this time on Dec 12 (grace period = Jan 12) but I leave on the 15th, 3 days after this new grace period ends. I tried to contact my sponsor but they won't answer and to change my ticket is too expensive at this point. If I leave 3 days after my grace period is over, will I have a problem with that? Will I be able to come back at another time? Besides the J1 visa I also have a tourism visa.
For any Visa related problems, you must feel free to contact "INS - Immegration and Naturalization Services" of US Govt.
I am sure they would understand that your intention can not be any violation in staying just 3 days more and they will allow you officially to extend it to 3 days. Better to get permission than to keep guessing how much will you damage your reputation as rule abiding visitor.
They do have fax numbers and you can keep a copy when you depart in case you have not received reply in-time.