Risk and Consequences of Overstaying a J-1 Visa

Hello experts, especially the very helpful Mr. Knowitall!

I have looked through the forum for a while, but haven't found an answer to my specific question. I'm an exchange student on J-1. No 2-year requirement and DS-2019 states May 15 2010 as end of program. D/S on I-94, which means that I'll officially have to leave the country by June 15. I'm aware that I can still apply for extension/change of status, which costs around 300$ according to my research. I could also head to Mexico or Canada for some time and get a tourist waiver, being European. Costs are similar.

I want to spend July 4th with a befriended family in Texas and leave soon after. I'll be out-of-status if I don't do anything and fly back home on July 6th. From your experience, how many days/weeks could I overstay without having to fear consequences upon future re-entry into the US. Would you advice me to take action and definitely not overstay at all?

Your overstay will disqualify you from the visa waiver program (assuming your nation is part of that program) and could complicate any future visa application or attempt to enter the U.S.