Many successfull former startups are currently well-established companies in BigData space. That means that their key technical competence is in handling the large volumes of data.
Question is: is this competence in the heart of the success of these companies or is scaling a commodity which comes somehow with the success?
In other words: for early Google, what was critical: PageRank or MapReduce?
I'm pretty sure scaling can be bought. User demand can't. So if you can only get one thing right, make sure you build something that people want more of. That will bring you resources which will allow you to scale.
Scalability is a technical issue that comes after the hardest part. If you are having scalability problems, then you are already pretty successful. Most of the time it does not happen. Make sure you find the right priorities about things to worry about. After you've found product-market fit, you can focus on scalability, but before that it's a waste of time.
Some things scale and some things do not. A business model might not scale well. In that case, you'll have problems growing to be very big. However, Alain is right that the most important thing is getting customers. However, make sure that you can handle an influx of customers (scale) or that big bundle you spend on marketing will only drive your company into the ground.