Can a baby be overly tired?

Liz • Baby #2 due 12/24!
My baby is almost a month old and for the past few evenings she's been crying nonstop. She's not hungry, her diaper is dry, doesn't seem to be gassy. I think she's been up too long and is just super sleepy. She's been up since 3pm, its now 10:40pm. I guess my question is can babies be overly tired, and just not able to fall asleep?