Once an extension of stay is denied, a foreign national must make plans to immediately depart the United States. The Customs and Border Protection website offers guidance regarding how long a person can remain in the U.S. following the denial of the extension.
“USCIS generally allows you 30 days to depart the U.S. starting from the date on the letter notifying you of their decision to deny an extension. If you do not depart within 30 days, you will be considered deportable. USCIS cautions that if you are refused permission to extend your stay, you may encounter problems with Consulates overseas the next time you apply for a U.S. visa because their computer records will indicate that you did not leave the U.S. within the time frame of your initial period of entry. Be sure to keep your rejection letter and proof of the date of your departure (a boarding pass is the best thing, but passport stamps showing entry into another country is also helpful) to give the consulate the next time you apply for a new visa. Having those may mitigate your apparent overstay and could improve your chances of renewing your visa without the five year restriction usually applied to people that have overstayed their visit.”