I'm sure it is an important part of the success mix, but I'd say the only thing you really 'need' is a great team!
As one angel investor put it:
"We’d invest in an A Grade team with a B Grade product, but we wouldn’t invest in an A Grade product with a B Grade team."
This premise holds if you replace 'product' with 'idea'.
FYI: The quote came from a post on one of my favourite blogs: startupblog.wordpress.com. He's done a series of posts on just how much the 'big idea' is overrated as a factor for success.
I say yes. IMO, the idea needs to be, at its conception, something that is beyond your capacity to achieve. I would consider that to be a "big" idea.
Your business endeavor is the bridge to your vision. In building that bridge your idea will be forged by the process of covering the gap that exists between where you were and where you wish to be. In the process of designing, planning, and executing the construction of your bridge, you yourself grow.
And when you arrive at the moment of crystallization, when you achieve the thing you set out to do, you realize it wasn't all that big an idea after all and you turn your attention to the "big" ideas that naturally grow out of the vision you have built.
Success would then be defined as, by virtue of developing your flexibility, creativity, determination, and innovation, spending your life in pursuit of your "big" ideas, building on top of success after success and learning from the failures that will invariably bar the way.
If you define a big idea as large enough to hold your dreams, then the answer is yes. As an example, I point to a service like LibraryThing. While it's never going to be big enough to be the "Facebook of Bookworms" (and I'm a lifetime member so I can say that), it's still a great idea and a big idea to those who have a passion for reading.
Your idea is big if it expands your heart or your mind and fulfills your passion.
That may sound a little woo-woo, but it's that kind of project that's going to get you through long nights of coding.
As a small business I think having a big idea helps motivate us. However, we get there one day at a time by working on generating and delivering lots of small ideas.