What is the relationship between the French and Indian War and the movements for American Independence?

As a result of the French and Indian War, the British had accrued a significant amount of debt.  Paying back the interest alone was going to require a significant amount of the empire's yearly budget.  Many in England felt that the colonists were not paying their fair share of the burden of taxation, especially considering the rewards that the colonists were reaping from the protection of Britain's powerful navy.  
The colonists, on the other hand, were beginning to feel culturally and politically distant from the mother land.  Decades of lax governance by the Brits had engineered an independent spirit in the thirteen colonies.  For this reason, when Parliament started to expect more revenue in the form of enforcing new and existing tax legislation, the colonists were not willing to pay.  The colonists felt that if they were to be taxed, they should have representation in Parliament to decide what the taxes would be and how the revenue would be spent.  
http://www.let.rug.nl/usa/essays/before-1800/french-and-indian-wars/effects-of-the-war.php