It is first important to understand that not all Republicans rejected a peace settlement with the Confederates during or after the Civil War, but it was a smaller group within the party that totally and completely refused and demanded a full surrender without conditions to the South. This group was called the Radical Republicans and they began around 1854 and went until after the Reconstruction of 1877. They were the ones who were responsible for the establishment of the Fourteenth Ammendment and they radically opposed any negotiations with the South on the basis of their being totally against segregation and slavery. Some other factions within the Republican party, including Lincoln, were more moderate and were willing to give in to some of the demands from the Confederates, especially ont he issue of slaves.
The reason for these radical Republicans not wanting to negotiate with the Southern Confederates, was that they refused to allow slavery to continue. They were pushing for all slaves in the U.S to be freed, for segregation to be prohibited, for rights for black people to be established in the United States and even went as far as pushing for civil rights, including suffrage, for African Americans. But the South, of course, refused these terms. This is why neither Radical Republicans, nor Confederate members would have been able to settle anything in a negotiation. There was no common ground for the toughest issue of all; slavery.
