Yes, I think most first-time entrepreneurs have a fantasy about how all they need to kickstart the viral growth is a bit of coverage in the major tech blogs. But the reality is that unless your site is squarely targeting early adopters (the ficklest of markets) and your product is knocking the socks of jaded San Francisco tech hipsters (well-nigh impossible against such perpetually-bored countenances), then this coverage is going to net you next to nothing.
In the reality you should take the time when your traffic is small to reach out to customers and get early feedback and polish the product as much as possible. The more work you put into based on real feedback from real users before the numbers get big, the greater the quality of the first impressions as your target audience trickles in.
Once your product is good enough, there are many ways to get users in. Press is one of them, but in my experience it comes on its own and is not worth putting much time in compared to more targeted user acquisition. In general, word of mouth will always always be the best, and that takes a great product.