Will I be illegal to stay in USA on Sep 29th and sep 30th?

I am currently working with Company A on L1B and my Visa will expire in Dec 2012. In the month of May 2012, Company B filed H1 for me and it got approved today.
Now the question I have is – The new approved H1 will be active from Oct 1st, 2012 i.e. Monday. So, If I want to join in company B from Oct 1st, 2012(Monday), my last day with the current company would be Sep 28th, 2012 i.e. Friday. So, do you think I will fall under illegal stay for Sep 29th and Sep 30th? Please advise.

I do not think that will be an issue, especially those 2 days are weekends. However, to be on safe side, please have it confirmed with any immigration attorney.