There could be other time-based methods to encourage students, rather than hard deadlines. For instance, suppose the class had a bag with unlimited (or large) number of question, and required each student to score 100 points to pass. Students would have unlimited number of attempts at quizzes/assignments, but their score decays with time (think HN submission ranking decay). That is, if you worked hard and scored 70, but then you were busy/away for a month, your score drops to, say, 50. So you are encouraged to finish the questions in a timely manner, but on the other hand, you can also make up for that missed month by putting more work when you are back.

With this method or a something similar, you do not "lose everything" when you miss a deadline. IMHO, "losing everything" for missing a deadline is part of the reason for the (exponential?) decay in the number of students participating in Coursera's PGM class[1,2].

[1] Based on PGM's "quiz's highest score" statistics, the total numbers of participating students are 6950, 3500, 2650 for week1, week2 and week3 respectively (other weeks' stats are not complete as of this writing).

[2] Another interesting stats is the ratio of perfect scores to all other scores: 25.2%, 34.3%, 49%. This could suggest that the deadline system filters out most students but the very top ones (assuming uniform difficulty of quizzes, and uniform quality of lecture videos/slides, etc.). This may not be what you want from an educational perspective. And, yet it may actually be what you want to support a business plan similar to Udacity- discovering talent. (see my comment below)