What to answer in an interview:
First, if you were asked to resign, and chose to resign, the answer is no. You left of your own accord.
If you were fired and it is reasonable to explain your firing as part of a downsizing, put it in that context.
"My company faced some major setbacks in the market downturn. As a result, they let off a sizable portion of their workforce, particularly for people like me in the position of ______. I was one of xx people to be let go (or for a small company, use percentages or say "3 people from a 10-person company"). My managers always thought very highly of me and even said they would like to bring me back when the company turns around (and will provide a very strong recommendation if you contact them)."
If you were fired with cause, due to documented misbehaviors on your part, you can take the following actions. If you can, reach out to the manager at the job from which you were fired. As graciously and respectfully as possible, tell them you are trying to learn from your past experiences. Ask how they would articulate your termination. Find out whether they would tell a prospective employer that you were fired in a future employment screening. If they will say that you resigned, you are in the clear.
If you need to say that you were fired with cause, deliver the answer as softly as possible. Make your termination not seem like an exceptional action on the part of the employer. Also, be humble and show that you have matured since then. “Unfortunately, I need to say I deserved it. I faced some tough family (personal) issues for a short period of time that impacted my work performance. I was also one of a number of people that were let go as the company tried to trim its costs. Obviously, I have grown since then.” If someone at your prior organization will speak well of you, you can add, “You are welcome to speak to so-and-so about my experience there.”
What about responding to the question, "Have you ever been asked to resign?"
It is pretty safe to answer this question with a no, even if you were asked to resign. If this previous employer is contacted, they cannot say that they asked you to resign without putting themselves in legal danger. In essence, the employer would be admitting to firing you. If you were fired, they owe you certain unemployment benefits, and since the organization failed to provide you with these entitlements, they could end up in hot water. So, you should feel pretty good about answering with a "no" in any case.