If you have a branch near you then print a copy of your Equifax credit report (Hopefully from this site so it has an accurate score) and sit down with a loan officer to see what they say. You may also be able to call their customer service line and have them direct you to the right person to help you on the phone. If your credit card approval was fairly recent they may still be able to review the information in their files. NFCU is very generous in working with people to rebuild from issues with other lenders. Worst case scenario you may need to wait a few months and show them some responsible behavior.
There is some unproven evidence that having an active banking relationship with them such as direct deposit and their being your primary bank seems to benefit your chances of approvals. I was not an ideal credit candidate when I switched to them about 3 years ago. Now I have the NAVCHECK LOC at max, a high limit CC and an offer sitting out there for a preapproved auto loan. And I am in the process of refinancing my VA mortgage with them. They are super friendly to work with.
Starting Score: 500's
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