Fining Me Is Not A Tax Increase

Barak Obama says a proposed fine for people who do not get the government run health insurance is not back-door tax increase. Instead he says, "What it's saying is, is that we're not going to have other people carrying your burdens for you anymore." I'm confused. If I chose not to get his insurance and I pay my own way, how does that make other people "carry my burden"? It seems more like they would carry my burden if I DO get his insurance. Can someone straighten this out for me?