I wish they had somehow connected the mandate to a tax deduction instead

Why is the government forcing me to buy a house?
Why is the government forcing me to get married?
Why is the government forcing me to have children?
Why is the government forcing me to give to charity?

They're not, but if you do those things, you get a tax credit (or used to). It seems easier for people to understand and accept when it's a tax deduction for actions that benefit society, such as purchasing health insurance would be. Buy health insurance, get a tax break. Don't and don't. Simple.