The responsibility for all Americans to obtain coverage would be enforced possibly through the U.S. tax system or some other point of contact between individuals and the government. Every individual would receive a certificate of coverage from their insurer to demonstrate that they are meeting their responsibility.
Enforcement of a responsibility to have health care through the tax system has advantages. The biggest advantage is that most Americans already have contact with the IRS through the annual filing of a tax return. Monitoring health insurance coverage through the tax code would take advantage of this existing relationship. One issue to be addressed, however, is how to deal with individuals who do not file a tax return due to their low tax liability. If a premium subsidy for health care was administered through the tax code, the non-filer issue would be significantly decreased because a number of current non-filers would voluntarily file in order to get the assistance.
If you don't understand why this frightens me, you're reading the wrong blog.