The primary reason it took Americans a long time to declare independence is that most of them considered themselves Englishmen, and as such, the King's good and loyal servants. Although independence was perhaps inevitable at some point, the primary cause was that Americans considered themselves entitled to all the rights of Englishmen; that this included their right to be taxed only by their duly elected representatives, rights which they believed had been denied to them. Even after the Battle of Lexingon and Concord, the members of the Second Continental Congress attempted reconciliation with Britain, maintaining their loyalty as the Kings servants, and asking only that they be treated as were their fellow subjects on the far side of the Atlantic:
The apprehension of being degraded into a state of servitude from the preeminent rank of English freemen, while our minds retain the strongest love of liberty, and clearly foresee the miseries preparing for us and our posterity, excites emotions in our breasts which, though we can not describe, we should not wish to conceal. Feeling as men, and thinking as subjects, in the manner we do, silence would be disloyalty. By giving this faithful information, we do all in our power to promote the great objects of your royal cares, the tranquility of your government and the welfare of your people.
We ask but for peace, liberty, and safety. We wish not a diminution of the prerogative, nor do we solicit the grant of any newright in our favor. Your royal authority over us, and our connection with Great Britain, we shall always carefully and zealously endeavor to support and maintain.
Thomas Jefferson, in the Declaration of Independence similarly stated that Independence was not a matter lightly regarded:
Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed.
Accordingly, Americans were reluctant to declare Independence not so much from fear of the power of the Empire, but because in many respects they hoped to remain a part of that Empire. It was only when reconciliation seemed impossible that they turned to war to free themselves.
What you have to remember when thinking about this is what a tremendously big step it was to declare independence. Britain was arguably the most powerful country in the world at the time. It was the richest and the most democratic. It would not have been obvious that it was a good idea to break away from such a country. Partly due to these factors, many Americans were reluctant to try to become independent. Even after the revolution started, something like one-third of colonists are believed to have been pro-British with another third or so relatively uncommitted to either side.
It would have been very scary to declare independence from the UK when being attached to it carried benefits and when the UK might well have been able to defeat your rebellion and punish the rebels. So it really is no wonder it took so long to declare independence.