If you submit a specimen and the USPTO refuses it, you will be asked to file an acceptable substitute within the determined time frame. If you do not agree with the decision of the USPTO, you can appeal it. Another option is to amend your filing basis from "used in commerce" to "intent to use" and submit your specimen later on.
If you fail to resubmit your specimen or appeal the decision, you won't be able to register your trademark. Before fully registering your trademark in the US, you must prove that you are commercially active in the US market. Failing to provide acceptable specimens will prevent you from obtaining your US trademark.
If your specimen is not accepted, you will receive a document called "Office action" issued by the US examining attorney explaining the issue and listing possible remedies.