What happens if John and Charles Wesley died in the clergy house fire on January 9th, 1709?
I think the effect is potentially huge. As much as Americans like talking about the Pilgrims on Thanksgiving, present day Americans would find the Pilgrims and their religiosity more than a little weird. Preaching in Massachusetts in the 17th tended to be very hierarchical, and the sort of strict Calvinism that the was the order of the day had very little room for the notions of self-improvement or redemption that describe a whole lot of American religiosity and culture, for good or ill, since the Founding. In addition, 17th century theology in the United States tended to be very analytic, looking at the texts of Scripture with a methodology very similar to the early sciences.(1) Emotional bursts of faith were actively discouraged, as were anything like a revival or gathered congregations - things that seem to define much of Protestant religiosity in the USA for most of the last two centuries. (Not that all of that old Calvinism has gone away - predestination is still a great tool to terrify your congregants into staying in the pews and filling the megachurch coffers.)
What changes this is the First and Second Great Awakenings, which among other things can be described respectively as "when the Methodists and Baptists get their foothold" and "when the Methodists and Baptists take off big." These are the Christian churches which seem more modern - a God of mercy, services that are deeply emotional, a focus on good deeds that occasionally gets accusations of being Catholic, and the nine-hundred pound gorilla: no predestination, and the idea that the person can move towards their redemption. The holiness movement is an outgrowth of this. As George Whitfield comes with the Wesleys, no Wesleys mean no him.
A huge amount of popular American society and culture has its roots in the Awakenings, and the holiness movement - the emphasis on doing good, displaying your inner holiness, and a populism that exulted the common man get their start in the US from the Methodists and the Baptists. So no Wesleys, a very different culture. Maybe a more hierarchical culture more respecting of its elites. A more Calvinist culture could be more accepting of social distinctions, up to and including chattel slavery. Who knows? But it'd be big.
(1) Not as crazy as it sounds - there's a reason you get figures like Newton coming out of the Calvinist churches during that time. The attitude was that you looked at what you thought were the works of God, period, with no emotional embroidery or wishful thinking. It was simply a worldview that wrapped various Greek versions of the Bible, and their translations, in with the natural world. Yeah, you can say they were stoopid foolz from teh stupidz... but it's still Isaac Newton, and more than a few others.