I used to run a playgroup with 65 moms. As the organizer I knew everyone and while I appreciated every group member I couldn't possibly, nor did I have the desire to, have everyone at my house for my son's birthday party. When I mailed (yes mailed) the invitations I specifically wrote on them, "Please do not discuss the party at any playgroup functions or with other group members as limited invitations were sent due to space issues and I don't want anyone to feel left out or be offended." Everyone who was invited understood and was respectful.
A few tips:
1) DO NOT hand out invitations at school. It boils my blood to see other moms doing this. Little children can't understand why their excluded when they don't get one and their is no reason to do this. If needed, ask parents for their home address during pick up or drop off and explain why.
2) Address this with your daughter, ask her not to talk about the party with friends unless she is at home on the phone or via email, etc.
3) Teach her how to be empathetic if it comes into play. Give her responses to use if someone asks her why they weren't invited such as: "I really wish I could have invited everyone but we just don't have enough space in our home, maybe we could have a sleep over the following week*." Or better yet, have her blame it on you, "My mom said I could only invite 6 people, perhaps we can get together for a mall trip next week*."
4)When dealing with these other mothers remember how it must feel to be them. It's hard for some mom's to deal with the idea that not everyone can be their child's best friend. If they do get wind of the party I would nicely say something like, "(daughter's name) and I really wanted to invite the whole class but unfortunately our home just doesn't have the space so we had to do our best to limit the party to her closest friends. Perhaps we can get the girls together for a trip to the ice cream shop a week after*."
*Stress the part where you/she makes plans AFTER the party. It will be awkward if they do a sleep over before then for everyone. The invited guest may feel compelled to "plead her case" during the activity if it comes before hand or your daughter might find it challenging to exclude her if she had a good time hanging out.
Either way, it's part of life and we can't invite everyone to everything. Just something everyone has to learn to live with.
Good Luck!