That's a myth from Democrat history books. The reason Confederates were worried when Lincoln was shot was that the Vice President, Andrew Johnson, had been vowing to hang the rebel leadership if he were President. Once in office, however, he quickly reconciled with his fellow Democrats.
In contrast, the Republican leadership at the time -- Stevens, Sumner, Trumbill, etc. -- were, for example, opposed to the death penalty for all cases, including sedition/treason. Far from wanting vengeance, they wanted the slave system completely uprooted. Most southern whites could not even vote prior to Republican Reconstruction.
I thought that's what I said.