The passage of Time can only be perveived by change. No change then no passage of time can be seen. The atom needs to deteriorate or the watch change, to know that it has occured. Not that it might not then exist mind you, but it wouldn't be perceived as such.
So the shortest unit of 'present' is the shortest unit during which a change of some sort can be shown to occur. This is the idea behind the plank as an empiric measure, but maybe something else can come along?
However this is only a unit of time, it doesn't describe what time is. A priori, I think Xeno's paradoxes cannot be beat. Fundamentally, the smallest unit of 'time' (whatever that is) would entail non-change, for any change would necessarily have a start and finish position. Multiples of 'instances' where no change occurs, when added together, can never give us change (and therefore time). So time is thus a product merely of perception and not necessarily a 'real entity' in any way. For all we know Parmedides and the Eleatics were right all along, and everything is an unchanging monistic unity; or our perception alters the material world in a Buddhist Sunyata sense; or maybe time is an illusion itself of infinite created universes only slightly different than the last; or only this very instant exists and there is no future and no past, only the perception that there had been or will be.
The only answer is to smash all the clocks. Time is an illusion of perception, so my being late for work and sleeping in, is merely convention and not fundamentally true. I was on time, or am on time, perpetually.