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).

Tom Paine no doubt is the most influential because even Bob Dylan sings about him: ...

    Just then Tom Paine, himself
    Came running from across the field
    Shouting at this lovely girl
    And commanding her to yield

    And as she was letting go her grip
    Up Tom Paine did run
    "I'm sorry, sir", he said to me
    "I'm sorry for what she's done"

Ouch. Dylan: America's tough-but-fair national psychoanalyst.

In a sense we are comparing apples and oranges. How do we compare On Civil Disobedience? The book toppled the British without firing a single bullet. At this point we would have to consider different timelines altogether.