There is a hostile power to its immediate south, meaning the United States will now for the first time need a large standing army and a large navy.
Which is really unfortunate, because the US may well embark on a massive campaign of military spending based around what it thinks is state-of-the-art technology (muzzle-loading rifles, smoothbore muzzle-loading Dahlgrens, wooden ships and Monitors), only to witness the Prussian victories in Europe using breech-loading artillery and rifles and then have it followed up with a global recession in the 1870s.
The EP was in 1862. Odds are any peace would be in 1863.
The Emancipation Proclamation was issued because Antietam was enough of a victory to justify it. With a peace in 1863, odds are there isn't an opportunity to issue an Emancipation Proclamation.
This hostile power has re-enslaved black union soldiers that it captured. Unless, as part of the condition of the peace, these soldiers were returned, it's going to be a BIG issue.
While slaves that have escaped to Union lines will be an issue, if there's no EP, would there even be black soldiers at all?
Are there any captured black soldiers with a 1863 peace? 1st Kansas Coloured Troops has a skirmish in October 1862 but loses only killed and wounded; 54th Massachussets starts recruiting in February 1863 and first goes into action in July 1863; 1st USCT doesn't muster in until mid-1863.
OTL there weren't that many blacks in northern states before the Great Migration. There are going to be a lot more blacks and thus a lot more republicans in the US TTL.
Or there are going to be a lot of laws preventing black people from settling in Northern states, like those of Oregon (Article 1, section 13; "No free Negro, or Mulatto, not residing in this state at the time of the adoption of this constitution, shall come, reside, or be within this state, or hold any real estate, or make any contracts, or maintain any suit therein; an the Legislative Assembly shall provide by penal laws, for the removal, by public officers, of all such Negroes, and Mulattos, and for their effectual exclusion from the state, and for the punishment of persons who shall bring them into the state, or employ, or harbor them," approved 8,640 to 1,081 in 1857) or Indiana (Article 13; "No negro or mulatto shall come into or settle in the State", approved 113,828 to 21,873 in 1851), or Illinois (Article 14; 'The general assembly shall, at its first session under the amended constitution, pass such laws as will effectually prohibit free persons of color from immigrating to and settling in this state,' approved 50,261 to 21,297 in 1848).
Unless the black population grew substantially (something which moderate Republicans and Democrats would have every reason to discourage) I don't see the issue of black rights being more than a niche issue which probably serves to split the Republican Party in the 1868 elections. If there was no EP in this scenario (which would mean fewer black troops) slavery remains legal in the remaining slave states and they'd be touchy about attempts to infringe upon it.
Just to put some numbers to this: the 1860 census shows the core Union (all states and territories except the 11 Confederate states and Kentucky) as holding 344,626 free blacks and 207,211 slaves. The Union retaining Kentucky tips that over to a slave majority - 355,310 free blacks and 432,694 slaves. Granted, you've got population movement during the period of the war and possibly some afterwards. However, you've also got the basic fact that many of those slaveowners are influential public figures, and that when the Civil War ended historically free blacks couldn't vote in 19 of the 24 Northern states.