The research base that developed the term "deliberate practice," (and, for that matter, more rigorously defined "expertise") comes from K. Anders Ericsson[1] and colleagues who contributed to the The Cambridge Handbook of Expertise and Expert Performance (2006), a book[2] summarizing research in many domains of human performance.
There are a lot of popular books on these ideas, but only a few take care to distinguish deliberate practice from playful engagement or routine performance by an amateur, and only a few look carefully at the definition of "expert" performance. What's rigorously defined as "deliberate practice" (with coaching and monitoring of fine details of performance) is very hard to do long-term for more than four hours per day, which is why the "ten-year rule" was the original expression of some of the earliest findings on the development of expertise. Your sleeping hours don't count (directly) for development of expertise, nor eating nor hours spent on other daily activities, so it takes years to accumulate 10,000 hours of deliberate practice with necessary rest and play in between sessions of practice.
[1] http://www.psy.fsu.edu/faculty/ericsson.dp.html
[2] http://www.cambridge.org/us/academic/subjects/psychology/cog...