The interviewer would like to see that you can be creative and mindful when it comes to marketing budgets. Whether you are working with an internal or a client budget, it's essential that you respect those funds and find the best way to work around those restrictions.
Now, we know that marketing professionals often face completely unrealistic numbers. There is no need to address this type of example in your response. Focus on a time when you were just shy of meeting a budget, but made a significant tweak, to save the day.
"I worked with a client last year who needed a social media campaign overhaul. Their budget was modest but do-able. I quickly realized, after analyzing the budget breakdown, that the design work allocation was unbalanced. I approached the client about using our internal design personnel rather than the third party contractor he had insisted on, in the beginning. He agreed, and I was able to bring his project in around 5% below budget."
"I often see clients requesting high-quality video work without the budgetary allowances required for such an undertaking. I want my clients to succeed, without overspending, so I will often make suggestions on how we can repurpose content, or use one piece of content in an omnichannel approach. Of the eight significant campaigns I have worked on so far this year, all eight have come in under or at the budget."