You'd change the entire history of the American West, directly or through butterflies. The last you'd get the same as OTL is the actions there during the Mexican American War.
- Sam Brannan never arrives with the
Brooklyn at Yerba Buena (San Fran), carrying Mormon settlers to California which tripled the population of the settlement. They brought the first flour mill, the first newspaper, the first school. Without the
Brooklyn, Yerba Buena remains a small village.
- Without Mormon workers at Sutter's Mill, all Marshall can use are Native Americans. These guys are probably not going to go sell their bits of gold at Yerba Buena, especially not when Yerba Buena doesn't even have stores to buy from (without the Mormons). Sutter gets to keep his gold secret, what will he do with it?
- If the gold secret does get out, it will do so slower. Not just because the diffusion of gold from Sutter's Mill to Yerba Buena is slower, but without the direction of Sam Brannan and his newspaper, the news of it won't get out! It will work almost entirely by the direction of Sutter, though I would think that after a while SOMEONE has to find out.
- Without the Gold Rush of 1849 and the rapid growth of population in California, the Compromise of 1850 isn't going to happen or have as much impact. Texas is a slave state unbalanced by another. Antebellum American history is going to be skewed significantly.
Enough about California. Consider the effects of the Mormon colonization of the west. They built roads and trails to the west, bridges, roadside settlements to help facilitate travelers. They brought great business to the west, buying up goods in forts and the isolated settlements already there, encouraging more investment to the area. They irrigated the Great Basin, created a huge number of settlements throughout the West, of which many became modern cities, and negotiated fair relations with the Indians.
Without this charitable, zealous drive to tame the West, its colonization is going to be delayed and slowed. American colonization to Oregon might be delayed enough so that Britain could get their claim. Many more will board ships to California once that gets started (later), taking the long voyage around Cape Horn. That might be a good thing, but it will, once again, delay the settlement of the West.
This will most likely change American history significantly, with different presidental elections, issues, choices, and the Civil War occuring differently, no matter how you take it. And you know what butterflies in the Civil War could do: Southern independence, or worse, continued concession to ideas of slavery.
And then you've got to consider the lack of Mormon charitable organizations. Sure, because we don't have such a huge membership, we aren't able to do as much. But we don't pay anyone for their religious duties, and we gather ten percent from the profits of every member, and thats a lot of money that is gathered and spent on charity. No more Mormon missionaries means more of a negative light of Americans in foreign countries, as missionaries out of the United States (and Canada and the UK) are really just a religious version of the Peace Corps.
Oh yeah, and no Battlestar Galactica.