Can You Get it Done Even Sooner?

We know that meeting our client's deadlines is critical, and doing what we said we'd do when we said we'd do it is a top priority for us--we'll do whatever it takes.  But even with every effort we can muster, we may find ourselves up against a deadline that's near impossible.  Take this actual email string between an engineer and a client, for example:

Client: "When will you be done with the project?"

Engineer: "I worked on it all night and emailed it to you early this morning."

Client: "Well, is there anything you can do to get it to me sooner?"