According to the Obamacare website (click here) the penalty for those who choose not to get begins April 1, 2014 and will be assessed on your tax returns.
There are a variety of challenges this law brings economically, morally, and constitutionally.
I find for myself that the moral issue that trumps God's law violates my conscience more than the economic hardship, the fiscal irresponsibility and the constitutionality of the law.
There are some alternatives provided through three health-sharing ministries. Click here for a great summary of the three.