Thanks to my American salary and Swedish consumption level, my basic needs can be met for many months even if my salary drops to $0. (Not that I actually want paternity leave - it sounds boring.)
So, I'll assume you're above the crossover point. In Sweden, we tend to think that everybody should be able to be home with their kids, not just the ones with enough income to save up..
The people at the very bottom actually have more time to spend with their kids. 80% of our poor (roughly our bottom 15%) are not in the labor force, for example.