In July of 1798, Congress passed β and President John Adams signed - βAn Act for the Relief of Sick and Disabled Seamen.β The law authorized the creation of a government operated marine hospital service and mandated that privately employed sailors be required to purchase health care insurance.
Short version: There's no proof from the historical record that Adams would have backed the idea behind the individual mandate in particular. But it is fair to conclude, that the founding generation supported the basic idea of government run health care, and the use of mandatory taxation to pay for it.
http://blogs.forbes.com/rickungar/2011/01/17/congress-passes-socialized-medicine-and-mandates-health-insurance-in-1798/
http://www.scribd.com/doc/29099806/Act-for-the-Relief-of-Sick-DisabledSeamen-July-1798
http://voices.washingtonpost.com/plum-line/2011/01/founding_fathers_favored_gover.html
http://www.common-place.org/vol-09/no-01/rao/