God bless the recruiters for what they do and the patience demanded of them.
That said none know absolutely everything about the navy and many lack some key knowledge to answer worthwhile questions from potential recruits. Especially when it comes down to those persons working in the nuclear field.
EM3 here currently in prototype training btw in case you are wondering from what basis do I offer an answer to your question.
The major disqualifying points are what you would expect: History of emotional/mental problems, certain physical handicaps, criminal issues, personal life issues (pregnancies,litigation in process, etc.), and a slew of other random disqualifying factors (anywhere from having braces on your teeth to drug use).
The important thing to consider is to not confuse something that disqualifies you from something you will be asked to comment on.
If you had knee problems but a military doctor says you are fit for duty: No problem.
If you failed a math class at some point in your life but provide a reasonable explanation either orally or in writing to a personnelman: No problem.
If you have debt but you have proven yourself capable of managing it: No problem.
I went through part of my training with a friend who had $92,000 in debt, one with $65,000, and one who had $25,000 because he bought a new mustang weeks before joining the navy so that he could have the interest rate on the loan lowered.
That you have debt is not an issue. How you have handled it is. Even if you've had years of bad debt and late payments if you decide to put forth a consistent and valid effort to take care of your financial obligations you will eventually receive your clearance and be no worse for the wear. I guess what I'm trying to say is that while there is a specific algorithm for deciding who is, without question, eligible for being a nuke, just because you might not fit into that does not exclude you from being one.
If you are honest during your recruitment phase and pass the standards to apply to become a nuke you will make it to nuclear field "A" school. If you show integrity and personal management skills you will get your clearance and make it to power school/prototype.
Hope that answers your question and if not feel free to message me and I'll respond as quickly as I can. The important thing is to realize I was sitting exactly where you are now just two years ago. I made it and, more importantly, I have not regretted the decision.