I came across this really great presentation and explanation on how to quickly do user research in the context of the startup. The presenter, Michael Margolis, is a Google Ventures partner and has been doing this kind of work for more than twenty years. He works with the GV startups to help them understand their users and to figure out how they should build their products in order to meet the needs of their users.
One argument that sticks out from his lecture is the reason for observing users. He argues that the importance of observing users is to understand the 'why' of particular user actions. He compares observing users to looking at detailed website analytics. Analytics will reveal what people are doing, yet it won't reveal why they're doing what they're doing. Seeing the metrics of a certain website funnel, or being able to see the data of people dropping off at a certain page doesn't give insight into the problem that might be causing users to drop off. Discovering the 'why' behind a certain problem will then reveal the solution.