The laws depend on the state, I had one little boy when I taught kindergarten who missed over 20 days of school. No medical problems, no special reasons why, he just wasn't there.
In Ohio you are not required to attend school until 6, so in kindergarten it is very hard to "fail" based on attendance since most kids start at 5.
If you miss more than 15 days of school in a year, (without documented medical reasons) you cannot "pass". Though there are sometimes ways around it in special circumstances.
In some cases without documented excuses from school, parents can even be fined (this isn't counting sick days, more like kids who just don't show up)
Yeah, I actually used to know a mom that kept getting letters from the school saying her kids had missed "x" days, and that she was going to be fined $500 per child if they missed anymore school. They were willing to work with her on days that the children were sick, but missing for no apparent reason was no longer acceptable. She used to keep them home because she was lazy, refused to get up and get them ready, and didn't make them feel that school was important at all. It was a really crappy situation, but I'm glad the school was forceful about getting it taken care of.