I don't think this is that uncommon. It just depends on how far grandparents live, and whether they have other grandkids. When our first child was born, both sets of grandparents couldn't wait to help out — it was their first grandchild, after all. As other kids have been born, they've had less time to do so.
>>gnicho+(OP)
My experience has not been 'we don't want to care for grandkids because we're so busy caring for our copious grandchildren that we're too busy for one'. It's more like "I want to go to Europe... too bad".