I sent in my exemption application and received it back for corrections, I sent the document back in November 2014 but I have not received my tax exemption number yet.
You'll need your Electronic Confirmation Number (ECN) from HealthCare.Gov to claim exemptions. If you haven't gotten yours back you are going to have to follow up with the Marketplace. If you don't have it by tax time, you can try filing for another hardship exemption using your troubles with getting an exemption as a hardship.
Not all exemptions need a confirmation number, so double check the list above to see your options.
In general there are a lot of exemptions and they can be very flexible. So do take the time to find one that will cover you.