The Second Continental Congress actually voted for independence on July 2, 1776--not July 4th. On the night of July 2, 1776 the Pennsylvania Evening Post published a statement that "This day the Continental Congress declared the United Colonies Free and Independent States.
On July 2, John Adams, wrote to his wife back home in Massachusetts that, finally, the Congress had adopted a resolution establishing the independence of the former colonies from Great Britain. Adams wrote his wife Abigail that he believed that July 2nd would be celebrated annually in this new country.
So why the confusion about July 4th? It was on July 4th that Congress approved the language of the Declaration of Independence, a statement to the world justifying the action taken by the Congress on July 2nd. The Declaration included the text of the July 2nd resolution in its concluding paragraph.
And who is Casear Rodney and why, except for natives of Delaware, is he lost in the "dustbin" of history? The Second Continental Congress wanted unanimity for its resolution of independence. The proponents of independence had resigned themselves to New York's perpetual "respectful abstention" on the issue but wanted to secure the approval of the 12 other colonies. Eleven colonies were in the fold with Delaware hanging in the balance. Delaware had a three-man delegation with two on opposite sides of the debate and the third, Caesar Rodney, very ill and struggling to balance his many responsibilities in Philadelphia and back at home .
Suffering from both facial cancer and asthma, Rodney learned of the split in the Delaware delegation. Resolved to end the stalemate, he embarked on an extremely dangerous overnight journey of 80 miles to Philadelphia through violent thunderstorms and torrential rain. He arrived on the afternoon of the 2nd, greatly fatigued, just in time to break the Delaware stalemate on the resolution of independence. Those who wrote about his dramatic entrance indicate that he stated the following :"As I believe the voice of my constituents and of all sensible and honest men is in favor of independence, my own judgement concurs with them. I vote for independence."
And so it was that the vote of one man, Casear Rodney, allowed these colonies to demonstrate unanimity and vote for independence on July 2, 1776.