Here is what I would do if I were you...

If I could manage to pull it off within the boss's expectations, I would do it first, and if need be, talk this thing over with him at a later time.

On the other hand, if it is absolutely beyond my capabilites/resources to complete the project before the deadline, I would bring this up with my boss, calmly and professionally, and ask for his input for a feasible solution.

As a rule, one does not win by injecting personal emotions/feelings into a work-related issue, not when the one sitting across the table is one's boss. Conversely, maturity and professionalism earn one credibility, not to mention good will in a case like the one at issue.