The big problem in America with voting is that election day is not a national holiday. If there should be any incentive to vote, there should be fines for employers who don't give election day off (not saying people cant' elect to work that day, but it needs to be a default holiday), or a mandated pay hike to employees working election day (say, doctors, police, utilities workers, etc that can't really have a day off).
But absolutely don't mandate individuals vote. Its their right not to. You don't get to go around telling other people how to behave if it doesn't negative impact you. And the people not voting now won't become more inclined to get involved because they are forced to, in the same way children aren't intellectually stimulated by being forced to go to public schools.
I could see your argument for having deliberation day or something, but there are other solutions for the problem of long waiting lines at the polling place. (I was 18+ and resident in California previously, so I waited those lines, too. I wasn't employed then, though.)