Mother Guilt

For some reason, I have this need to get this ugly chunk of coal out of my heart, which has been smoldering in the corner for about a year. I'm not sure what else to do with it aside from barfing it up onto the blogosphere, hoping for some cathartic release in the process.
I have this mother guilt. When I am maxed out on my ability to play with my child, I let her watch television. Not 8 hours a day, but probably 3 hours. Not consecutively, but split into chunks. I have done what I swore I would never do; I have allowed the television to serve as an electronic babysitter, when I need to get something else done that does not or cannot involve her (like showering, or cooking dinner). All that I have read suggests that television isn't good for small children. I could be risking her developing ADHD or associated attention-oriented problems. Yet, I am at a loss for what else to do.
I am introverted. When I was a child, I spent hours upon hours entertaining myself. Drawing, reading, playing with clay. Playing outside. Making forts for myself. I grew up with no siblings, and as a young child, few neighborhood friends. It wasn't a kid neighborhood, from age 2-9, before we moved to a new area. I like to entertain myself, but Hootie does not. From nearly the moment she awakens until she goes to bed, she asks me constantly to play with her. There are many activities I do enjoy doing with her - drawing, reading to her, playing with her playdoh (sense a theme?) and many others. We go to the park, play outside in the sandbox, and I get her involved in helping me with various chores around the house as well. What she wants to do more than anything, however, is pretend play - with her little figurines of Dora and Boots and Diego, and the various animals they can save and rescue. I have the patience to do this with her once or twice a day for about 10 minutes, until I am so bored my eyes roll back in my head. She wants to do this over and over, and I just don't have it in me.
She's going to be an only child, so there won't be another little sibling around for them to entertain each other. That leaves friends, and me. I have gotten her involved with preschool 3 mornings per week to get a lot of social interaction with her peers. We have other playdates with other friends too. But when we're at home, just the two of us, she doesn't much like to entertain herself; she wants to be interacting with me nearly all the time. I have no idea if this is normal, or if it is something she learned from the way I interacted with her as a baby. It's obviously a need I feel responsible for fulfilling, because it breaks her little heart when I tell her sometimes that I don't really want to play. Hence, the guilt. I don't know if a good mother is SUPPOSED to play with her child all day or if it's alright to say no, and let the chips fall where they may. I have tried to teach her HOW to play on her own, but the second I leave, she complains that she wants to do said activity WITH me. Not by herself. She claims in her drama queen way "I need someone to play with me! I'll be SO SAD if I have to play by myself!" and she'll run to her room, sit in her time-out chair, and sob. I feel like I must be cruel, the times I am just unable to continue playing for hours, given the heart-wrenching reaction I get from her.
Thoughts, anyone?