At that time, most Americans still saw themselves as British subjects. People weren't American once the Declaration was penned -- there was still a war to win.

If the 'most influential American writer' means 'the one most important to the US becoming its own country', then the answer is Thomas Paine. His American Crisis papers buttressed the flagging revolutionary movement and made the common folk actually care. Before Paine's propaganda, the majority of colonists saw themselves as British subjects and the fight for independence was only really supported by the landed gentry.

The American Crisis papers made the common folk care, and without them there likely isn't enough popular support to win the war.

Paine > Jefferson as pertains to the American cause (and Paine > Jefferson as person).