Time

If time is not an object how can the phrase "I don't have enough time" be considered possessive?

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The word "time", in this use, is what we call a "mass term", as opposed to a "count noun". It's like "gold" or "water" rather than like "tree" or "dog". Note that you can't say "I don't have enough dog", unless you're serving dog for dinner. You would have to say, "I don't have enough dogs", perhaps, to run the Iditarod. Similarly, if you say, "I don't have enough times", then you mean something quite different. For example, you might mean there aren't enough appointment slots to see all the students.

Exactly how we should understand the behavior of such expressions is a difficult question, but one doesn't suppose that "gold" refers to an object just because one can say, "I don't have enough gold". The other thing to say is that the relation indicated by "have" in such constructions is incredibly various. This point has often been made with respect to the possessive that is indicated by "'s". So, if we speak of "John's bike", the relation between John and the bike can be many things: It may be the bike he owns, or the one he was riding ("John fell off his bike"), or the one he built ("John was fired because his bikes all had defects"), or the one on which he bet in a race or perhaps sponsors ("John's bike finished third"). I'm sure you can come up with lots of other kinds of examples. So one has to be careful in drawing conclusions from the occurrence of such expressions as "I don't have enough time".

It may be, too, though I'm less sure about this, that this phrase is an idiom, like "kicked the bucket".

In addition to the points that Richard makes above, we might consider the fact that the expression "time" functions oddly in lots of constructions. Having too much time on your hands is quite different from having too much lotion on your hands, having time on your side is different from having Jack your side, and time's running out is different from Jill's running out.

It might also be useful to remember that we should always be careful not to put too much weight on the surface grammar of our language. Lewis Carroll got a lot of mileage out of this, e.g., in Through the Looking Glass:

"I see nobody on the road," said Alice.

"I only wish I had such eyes," the King remarked in a fretful tone. "To be able to see Nobody! And at that distance too! Why, it's as much as I can do to see real people, by this light."

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