Americans for Tax Reform notes that when Barkycare's individual mandate kicks in in 2014, we'll get to fill out a brand new tax form:
This new tax information document must, at a minimum, contain: the name and health insurance identification number of the taxpayer; the name and tax identification number of the health insurance company; the number of months the taxpayer was covered by this insurance plan; and whether or not the plan was purchased in one of Obamacare’s “exchanges.”
This will be required as an inclusion in your April, 2015 filing. Your insurance company (if any) will be sending these data along to the IRS. If you can't prove coverage, you'll get to pay the fine for failure to comply with the edict.