You know, growing up I don't remember a whole lot of times where my mom, or any adults for that matter, getting down on the floor and playing with me. I was an only child, and my mom was a single mom who worked her butt off 24/7. I was always surrounded by cousins and friends that I would always play with. It wasn't very often a grown up would be involved in play with me.
....and I think I turned out alright!
I think there is far too much pressure on parents, especially moms, to constantly be entertaining their children. I think a lot of a mama's anxiety, stress and feelings of inadequacy comes from feeling like they aren't doing enough with their children.
Yes of course, get down and play with your children! They absolutely love it! But don't worry or stress when you want to sit for a little bit, watch a show, do some laundry, clean up the house, make dinner, read a chapter of a book while your children are awake. They'll be just fine! They learn so much playing on their own! Also, if you have more than one child then, hey, look at that! They have an instant constant friend to play with! Don't stress so much, little mama. Your children love you and think you're the best mama out there! Don't overwhelm yourself too much. Do the best you can!