The easiest solution to 'child care' -- allow children to come to the office. Most people have cushy office jobs. Kids 0 - 5 do not take up much space.
Parents can take staggered lunch breaks to watch the children. Children would be in a common area that'd be appropriately gated off. In dual-income families, either mom or dad can take the child to their office.
Benefits:
(1) Both parents can work and be with their child
(2) Children see adults working, not just playing. This is good as children want to be like adults
(3) Non-parents get to spend time with babies and children, which is wonderful!
(4) For nursing working mothers, having the baby there would make nursing much easier than pumping. Babies could even be given little bassinets to sleep and wiggle around in near mom and dad, if they want that.
(5) The child/children can share in mom and dad's lunch.
(6) Cute babies in offices!!! How great is that!?
Speaking from personal experience, when my colleagues have been forced due to circumstance to bring their young children in to the office, the experience has always been positive. However, my colleagues seem worried that one of us may be offended and apologize incessantly. We should stop this and just make it a policy that children are allowed in-office. I mean, a lot of companies I've worked at have allowed dogs, which can't be potty trained, don't wear diapers, and sometimes bite people. Why are children treated worse than dogs?
EDIT: responses to this thread are the #1 reason why we will never have affordable childcare. Americans, as a group, highly highly dislike children, even if they won't admit it out of fear of sounding like a misanthrope.