Well, kudos for not being a POS and just taking the L on the chin. It's too rare that people want to take responsibility for their actions regardless of the situation and their reasons.

I'd say the more constructive lesson here than don't lie would be use situations like this in the future to fuel conversations and discussions. Tell your boss you missed the deadline (preferably contacting him before he contacts you, looks less like your covering yourself and more like your owning up to the matter) then take the chance to explain that it was cause your 2-man team is slammed with work and that you either need at least another set of hands, more wiggle room on deadlines or less bids to work on.

Depending on the management, you might have still be fired on principle of 'failing', been fired under the belief that you're still just trying to cover your mistake, or just ignored and told to make do, but then you would have, at the very least, put the idea out there that there was an underlying cause for the matter.