In the TOS episode "The Paradise Syndrome", Spock claims:
I am not hungry, Doctor. And under stress, we Vulcans can do without sleep for weeks.
In Voyager "Muse", Tuvok says something similar:
As a Vulcan, I can function without sleep for more than two weeks.
Although this doesn't give a number of hours, I feel it is relevant to your concern about "functioning adequately" — it suggests that Vulcans can function adequately without any sleep for a number of days before seeing any subsequent decline in their performance.
Also, while not sleep exactly, Odo must return to a liquid state every 16-18 hours — a fact which is regularly repeated in DS9. It is unclear, however, if this extends to the rest of the Changelings (many of whom have superior shapeshifting skills).
When he's deprived of his down time, he doesn't function very adequately: