I've always wondered if the Patriots were operating with political legitimacy derived from, at a minimum, the tacit approval of the majority of the colonists, or if the revolution was largely a unilateral action fomented by the wealthy elites of colonial society. For example, did the average colonist get to vote on whether their colony/state would attend the first Constitutional Convention?
The war with England started in April of 1775, well over a year before the colonists declared their independence. For most of 1775 many colonists believed that they were engaged in a civil war. They were not fighting to become separate from England only that the colonies be seen as equals with England, not ruled over by England.
According to Eric Forner, by the end of 1775 most of the ruling class of Massachusetts and Virginia were for independence. Other southern states were leaning towards independence. In New York and Pennsylvania their was no consensus of either remaining loyal to the crown or breaking away from England.
However by the time that the Declaration of Independence was made in July 1776 it is safe to say the average colonist was on board with Independence. This is often attributed to Thomas Paine's Common Sense pamphlet which appealed to the common man in the colonies. It is estimated that over 150,000 copies were sold in the first half of 1776.
The Members of Continental Congress were chosen by the legislatures of the individual colonies. The members of the colonies legislatures depending on the rules of the individual colonies but were mostly voted on by the colonists that could vote at the time(white males).
I should also add that war broke out between the first and second Continental Congress. The first congress had only decided on giving a list of grievances to England and to start boycotting more English goods if they demands were ignored. They had not made any plans to go to war with England.
Source: Give Me Liberty: An American History by Eric Foner