"Time is of the essence"… of what?

According to my New Oxford American Dictionary (2nd Edition), the phrase of the essence means

critically important

When it is said, "Time is of the essence," it is implied that time is in short supply or it is of the utmost importance. Therefore, if this statement is used with regard to a certain task, then that task must be completed as quickly as possible, and with a sense of urgency.

Anything can be of the essence in any given situation. Examples:

• Your concentration will be of the essence here. Put your mind squarely to the task at hand.
• A keen interest in this job is of the essence, otherwise you lose it!
• Consistent hard work is of the essence in this course; don't fall into lassitude.

"Time is of the essence" is a phrase used in contract law. It means that whoever is fulfilling the contract doesn't have limitless amounts of time to get around to it. For more than that, you'd have to consult m'learned friends.

I would guess that "time is essential in this project" would sound logical and appropriate to your situation.

Note that the word essential is directly derived from the word essence; "of the essence" is one way of adjectivizing essence, and essential is just another way of doing so.

We do similar things with many words. A couple examples:

• "Talk about something of substance" vs. "talk about something substantial".

• "A statement of fact" vs. "A factual statement".

• "I did it by accident" vs. "I did it accidentally" (in this case we are adverbializing).

It so happens that, nowadays, "of the essence" is rarely used, while "essential" is common. "Time is of the essence" is one of the few phrases that retains this construction, and so it sounds odd, but etymologically and structurally, it is straightforward.