You will see an Alert in the program titled Error or Omission: Missing Form 1095-A if you indicated in the return that you purchased health insurance through a government-sponsored Marketplace during 2019, but have not yet entered the information from Form 1095-A in the program. This Alert will prevent the electronic filing of the return.
Anyone that purchases insurance through the Marketplace will receive a Form 1095-A. However, below are 2 of the main reasons why you may have been informed that in your situation you will not receive a form, even if you believe you signed up for Marketplace insurance:
For both of the situations described above, you would change your answer to whether you purchased health insurance from the Marketplace to No (as that question is being asked solely for purposes of calculating any Premium Tax Credit on the return).
It is possible, though unlikely, that the call center at CMS is providing incorrect information (in telling you that you would not receive a Form 1095-A). However, if that is the case, the CMS would then want to know the time of the call and who you may have talked to so they can prevent this in the future.
If you sign in to your HealthCare.gov account (or your state-based Marketplace account), you would be able to confirm if your Form 1095-A exists as it would be available to you online.