I work at a very small company (less than 10 people). I am the only person that is able to do the work that I do there. However, I just graduated college and they are expecting me to work at a pace far beyond my skill set and also learn quickly on the job. I have recently switched softwares to do the GIS Mapping so that it could perform a new capability. That being said, something I had programmed using the previous version now won’t be available and I would be expected to quickly learn a new programming language in order to migrate the tool to the new software. I have expressed this concern already to the immediate supervisor and he can see that I am struggling. However, I am constantly being given more work as the head boss is constantly marketing and reaching out new clients. I feel I am falling further and further behind and don’t really have anyone to turn to. I also am getting paid very low-at an entry level and even at the low end of that. The head boss has also ridiculed me and told me that I have a slow learning curve when I would even stay late to finish projects that he asked for. I just feel uncomfortable keeping up and disagree with the work environment. That being said, I’m very afraid of quitting before things are done. Is it acceptable in my situation?
Sounds like you will never get things done. By the time you finish this even more will be piled on.
Look for another job is a last resort but I think that is where you are.
I’m very afraid of quitting before things are done.
It seems as if there was no time when all your work is done. This means the perfect moment to quit will never be, from the view of the company. What about your view? You already have left this place in your dreams, right?
Is it acceptable in my situation?
See the first comment to your question, the answer may depend on the region you are.
Apart from that, what should be not acceptable? The situation you describe is underpaid and overworked. If it really is, can you state a reason why you would like to stay there? Except your attitide towards work which is laudable! But there is not only the company, you are there too!
If the question is only about how to quit, then quit in a way that noone can tell you had left a mess behind you. Don't quit right now, leave a little time so you can clean up your stuff. You can mention that at your next employer.
Is it acceptable to quit with a lot of work still not done?
If your employer makes it difficult for you to succeed, that is your employer's problem, not yours.
Think of it this way -- your employer would not feel any sense of obligation or loyalty to you if they decided you were no longer needed.
Firing you would be a purely business decision, and the unfinished tasks would still need to be done. They would simply hire another person to continue the work.
You should therefore not feel any sense of obligation or loyalty to your employer, especially if they are not giving you any reason to do so.
If you decided to leave, they would simply hire another person to continue the work.
The short answer to your question is
It is acceptable to quit in your position. But that is because in the USA, it is acceptable to quit in any situation. There may be bitterness and they may try to harm your future career (especially if you quit with little or no notice), but employment is not slavery and you are free to leave at any time.
That being said, if you are willing and able, and you trust your leadership, you could try telling them that you are doing your best but are being given more work and deadlines than you can be expected to complete.
If you are not willing or able to talk or you do not trust your leadership to have a discussion about this without it becoming adversarial, you should begin your job search immediately. The usual advice applies: try not to quit your job until you have a new one lined up with a start date agreed upon.