In Common Sense (I believe it was), Thomas Paine wrote that it was inevitable that the British would lose/withdraw if the Americans simply continued to resist. He pointed out that each British soldier had to come a long way to get to the battle, and if he had to replaced another guy had to make that trip. As did their supplies and weapons. He pointed out that, while they could control the cities, they could never hope to control the countryside, which would make transfer of troops and provisions very difficult. Eventually the expense and impossibility of the task would defeat them.
The entry of the French made that cost go up.