You cannot stay in the U.S. unless you are able to change status before your J-1 expires.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
I would also question your understanding that you can legally stay in the U.S. until the H-1B start date of October 1. There is no "gap cap" protection for those in J-1 status as there is for students in F-1 status (see http://www.uscis.gov/portal/site/uscis/menuitem.5af9bb95919f35e66f614176543f6d1a/?vgnextoid=7f1a046c43360210VgnVCM1000004718190aRCRD&vgnextchannel=68439c7755cb9010VgnVCM10000045f3d6a1RCRD).
There may be a way to remain in the U.S. until October 1 (when you will be able to begin your employment). You should consult with the attorney handling the H-1B petition on this matter.
This is only a preliminary response to an inquiry, based on incomplete information. Helpful advice and counsel can only be provided after you have discussed your case with Mr. Bach, he is familiar with all of the circumstances of your case, and the advice is provided in writing. Any opinion provided here should not be relied upon for any purpose. No attorney/client relationship is formed until you have formally retained our law firm to represent you. We are not responsible for any action or lack of action you take based on this preliminary response.
I agree with my colleagues.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.