I hear this all the time. Frustration echoing in the voices of mothers everywhere, as they try to do it all. My reply is basic and simple, stop making excuses. Acknowledge your life is very demanding, but remember we are all in this together. It's a conscious effort and a conscious choice to maintain a healthy mind and body.
Exercise takes a little creativity and a little dedication.
With new moms suffering from sleep deprivation, exercise is the last thing on your mind. The perfect solution for a new mom is to put the baby in the stroller and go for a walk for 20 minutes everyday. This will get both mom and baby out of the house. Fresh air and the outdoors do wonders for your mind and body. Another idea is to look for a Mom and Baby exercise program in your area led by a certified instructor that you could attend.