For each API , there is a different error code that indicates that the sender is illegal or invalid for this message:
SMPP API - Rejection code 10 - "Source Address - Submission Control Failure"
REST API - Error code 15 - Illegal Sender
For messages to the US or Canada, the sender should be a US or CA virtual long number. If a different sender is submitted, the message will be rejected with the one of the errors above, depending which API is being used.
You can purchased numbers from within the Dashboard.
Please see USA : SMS Features & Restrictions for futher details of the restrictions in this market.