Balancing on a worklife

Since starting my new job there has been much discussion on work-life balance. It is something that my new company says that it takes very seriously. But they also work very hard and are incredibly successful - so either they are time management machines or the right hand is writing checks that the left cannot cash (it's mixed metaphor Monday!)

Either way, it is impossible. Maybe it is because I am gearing up for the first huge test of my new job or maybe because I am absolutely terrified of people thinking I do not work hard enough - but Sundays seem to be reserved for football and laptops.

It is not that I don't have a social life, I do! And I often spend parts of weekends enjoying it - but no matter what, the first thing I do every morning is jolt out of bed and think about all the things I still need to get done. The second thing I do is check my work email. 

My question is - how do you stop? How do you stop this cycle? How do you let go of the fear of failure enough to stop having it be in the forefront of every thought you have every hour of the day? 

I know that there is no way for me to stop now. I have two more weeks of living like an imminent heart attack before the situation can even be addressed. But after that - what do you do?