Assuming the airline could see what time your 1st flight arrived and that you had plenty of time, I'd be surprised if they reaccomodated you for free. Now you're taking up two seats (the one that went empty and the one you'll be sitting in that next morning), assuming no one was on standby for the seat on the flight you 'missed'.

Frankly it wouldn't surprise me if you had a reasonable amount of time if the airline cancelled the rest of your itinerary as a no-show.