The Confederate States collapse by the middle of 1863 as Conscription is opposed by the President and as the individual states look to their own defense, 'hanging separately' rather than hanging together. Stephens was a strict Constitutionalist and supported States Rights against any move toward centralization or central government power. He was therefore IOTL estranged from President Davis and exiled himself home to Georgia.
The result is, conversely, indeed probably the better outcome for the CS as a previous poster posited. An early victory forecloses on Emancipationist sentiment, possibly the Proclamation itself. The 'peculiar institution' is severely weakened but may eke out a dying existence into the 1880s, ending due to a lack of labor and exhausted land as well as territorial prohibition.
The political effect of early readmission is, with Tennessee, Arkansas, Louisiana and likely Virginia and North Carolina voting in 1864, a Democrat victory of the Seymour type. No Reconstruction or Freedmen's Bureau. By 1868, with all the seceded states back and slavery dying, political debate on the other issues - capitalism, internal construction etc (railways and tariffs). It is more likely that the Southern Transcontinental Route will be chosen (easier connections and symbolically and militarily binding the country) either alone or in parallel to the Northern Route. The Republicans may well retake the White House but the battle of ideas will be strongly contested as the U.S. is still tied to old ways. Pretty much only Slavery, Secession have been solved. The McKinley-Bryan battle will take place later I imagine, as the period of Republican dominance that pushed the country into a state where Industrial Capitalism and new ideas could win does not occur.
On the foreign front, will the U.S. put Juarez back on the 'throne' in Mexico? The French adventure will be scotched practically in the cradle, but will the Democrats be willing to restore a mixed-blood Indian and rabble-rouser to a failed Presidency? Will Lincoln's government, notwithstanding the great man's public support for the mestizo? Other than that, the United States will be as isolationist as historically. The conquering of the West will I expect take place largely as it did historically - on the one hand, the war finishes earlier, on the other devastation and disruption isn't as bad so there is a little less drive to move. One possible change is a lot more black emigration west from ex-slaves and runaways (the Dred Scott decisions and Fugitive Slave Laws are moot and the Territories are free territory where slavery is not presumed) and concurrent colonisation of Liberia, a government-sponsored project to lance the boil of black presence in the US, blamed for the war. So we could see the West 5% black (given 10% of the total population, that would be several times historical levels) and total slave and free-black population reduced by a quarter. Black codes will exist in the North to encourage the emigration of blacks from those States. It will be a significant political struggle which, outside of New England, will be successful.