The laws are quite strict in this regard. Immediately following the application denial you begin to accrue unlawful presence and must depart the U.S. In anticipation of that happening, you'd be well advised to discuss options with an immigration attorney.
Attorney Khurgel is a former USCIS and State Department Embassy Officer. His comments on Avvo are general advice, and do not constitute an attorney-client relationship.
The laws are clear and unforgiving in that regard. Immediately upon the issuance of a denial decision you are deemed to be out of status and begin to accrue "unlawful presence" in the country and consequently must depart ASAP. A period of 10 days after your having received the denial notice is reasonable, but a few more days will not make your situation any worse than what it is going to be once a denial decision is issued.
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
I would not remain in the US for over 10 days if your extension is denied.
Mr. Shusterman's (former INS Trial Attorney, 1976-82) 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.