Here's how it works. The instructor submits to NAUI your course completion info, and NAUI sends out the card (usually to your instructor). So if you don't have the card after a couple of weeks, then...
1. The instructor called you to tell you to pick up your card, but you didn't get the message. Solution: Call/go back to the instructor/dive facility and request the card. "Oh sure we've got it right here!"
2. NAUI sent it to you directly but the mailguy gave it to Aunt Maude 3 blocks down the street. She's been breathing 40% from her medical bottle instead of you breathing 21% from an aluminum 80. Solution: Contact NAUI and get a replacement card.
3. The instructor never managed to get around to doing the paperwork, and you are in Purgatory until you make something happen. Solution #1: Contact the instructor and find out why you're getting the runaround/bumsrush. Respectfully request you get what you earned and paid for. Solution #2: Contact NAUI, tell NAUI Headquarters the instructor is giving you the runaround, and they will be happy to light a fire under the rump of the lout. If s/he isn't professional enough to resolve it, NAUI Headquarters will help you solve the problem.
4. You forgot that you never actually finished the class. You still have to return that BC, take the last test, or pay the 50% that you forgot about. Solution: Finish up the loose ends and complete the course.
Most of the "no card" scenarios fall into one of these 4 categories. If your experience is different, don't hesitate to provide more details. Generally its a simple error in communication.