Life is about how you respond. The average person will have 13 careers in their lifetime, at least one will be as an employee. Just like in poker, how do you know when it's time to step away from a position (fold)?
I believe it comes down to "fit." Character and competence are important, but you need to find a role that suits your individual strengths and fits within the team structure. You may be on the right bus (company), but ask yourself, "Am I on the right seat (role) on the bus?" Put your pride aside when it tells you "I can make this work." Your job should be challenging, but know your strengths and limitations. Be true to yourself and to your employer about how effectively you are contributing. If you're not producing at a high level because it's outside of your skill set (and you won't get trained properly with a generous learning curve), do the right thing and step down.
How do you exit properly?
Be gracious and honest. Don't burn bridges you might cross in the future. Think of your career as a sub-category of your personal network. Last week I addressed the concept of work-life balance, where the lines of your career and personal relationships merge together. Just like posting information on social media, what you say and do after leaving a job leaves a permanent imprint on the future of your career. Approach your supervisor and share with him/her why you don't think your current position is a good fit. At that point, you have done your part (regardless of their response) so let the cards fall as they may. Your results are a reflection of your competence. The way you handle yourself is a reflection of your character.
This post hits home for me because in the past 6 months I've stepped away from two opportunities. I went in with an open mindset, but after a short amount of time, it was clear that I wasn't a good fit for the position(s). In both situations, I had honest conversations with owners I have a great amount of respect for. Even though I would have liked it to work out differently; it was about doing the right thing. During our conversations, what mattered to me the most was respecting the person across from me and maintaining our relationship. There were points where I felt weak and vulnerable, because my ego wanted to make it work, but in the end we came to an agreement that what was best for the organization(s) was that we went our separate ways for the project(s).