1 -- you are not just out of status, your stay will start to being "unlawful" if you are staying in US beyond I-94 expiry date. As you continue to accrue unlawful days, the downside can be quite severe.
2 -- if your attorney has filed a non-frivolous H-1B extension and requested for a Nunc-Pro-Tunc relief explicitly, USCIS may forgive the lapse in terms of filing.
------ If USCIS forgives and approves both the H-1B and extension of status (with an updated I-94 at the bottom of I-797), you are good.
------ If there is a gap between the I-94 begin date and the previous H-1B expiry date, USCIS did not forgive the unlawful stay but allowed you to continue to work for the employer without getting a new H-1B stamp.
------ If USCIS only approved the petition but not extension of status, you have to get a new Visa stamp and reenter before resuming to work for your employer
------ ensure that your petition was/is filed on a premium processing basis, for faster adjudication. Even if it was not filed on a premium processing basis now, you still have a chance to send I-907 form for a pending petition. Premium processing costs $1000
3 -- During the pendency of your H-1B extension, you are not technically authorized to work for the current employer
Bottomline, you will need to act fast.