What almost prevented the Declaration of Independence?

The biggest single problem was that the southern states were adamant that the Declaration must not condemn slavery. Even though slavery existed in most of the states, the delegates from the north wanted to end it once and for all. It became clear right away that delegates from at least 5 states would not sign up for that.

A second huge problem was that nearly a third of the country, including many prominent businessmen, politicians, and ministers, were strongly loyal to the King. Every state had a Loyalist group and in some states these were very strong.