The thing to realize is your (I am presuming) inflexible job was probably as responsible as your kid. They should let you work very flexible hours if you just had a kid unless by nature it just can't be done for that job.
Reasonable assumption but in this case I was able to be flexible enough. The problem was my child not sleeping more than a couple hours at a time and our stupid adherence to the "baby should sleep in a different rule" in the US.