If your family is just too busy to clean during the week, designate Saturday or Sunday as a group cleaning day. You'll be surprised just how much will get done when no one is rushing off to work or school, particularly if you set a firm policy that no one leaves the house until it's clean. Use this time to complete big chores that you can't fit in during the week, such as cleaning out the oven or the fridge or washing the mountain of laundry that's been steadily piling up. Even younger kids can help with jobs like dusting, picking up toys and vacuuming.
As you clean, reinforce to your kids (and spouse, if necessary) how quickly you could be done if everyone picks up after themselves throughout the week. Point out areas where they could make small changes each day -- like taking out one toy at a time and putting it away when they're done -- to free up a lot more free time on the weekend. If you don't mind a slightly messy house during the week and your days really are jam-packed, just knowing you have a regular cleaning day ahead can make it easier to ignore feelings of guilt on days when you can't seem to find the time or energy to wash the dinner dishes.
When the job is done, consider following up with a fun family outing as a reward for everyone's hard work.