Wow, this is making me feel so much better about my daughter's January birthday! Planning a party while busy with Christmas preparations is one thing, but having the party sounds a lot worse!
Honestly, I sympathize with wanting "4 warm bodies" or the like. With little kids, sure, sometimes they have super close friends. But sometimes? They just like playing with other kids. My oldest is about to make her 6th major move in 6 years. For her 4th birthday, we were having trouble coming up with kids to invite. She was so excited about having a birthday party... cake, ice cream, a pinata, games, etc. The issue was finding other kids to invite, especially when only one of her friends could come. It's just hard to really play some of those games with two kids, and she'd been waiting all *year* for the chance. (I ended up calling a friend who had kids just a bit older. She brought over her daughter and the daughter's friend, so there were two more little girls who played with mine at church, even if they weren't super close friends.) Thankfully, this year we've been in one place for 18 months or thereabouts, so she's got plenty of kids to ask.