Reddit mentions of The Historical Atlas of the Congresses of the Confederate States of America 1861-1865

There weren't any political parties in the Confederacy, and that's one reason posited by historians for why the Confederate government was so weak. There were no party lines to rally to, or party positions to uphold, or party infrastructure to call on. Not the way that the Union government called on Republicans. And there was no organized opposition to funnel discontent through, the way that the Democrats operated in the North. At least, that's what James McPherson suggests.

That said, rough factions did exist in the Confederate polity. For details there, look to Kenneth C. Martis and Gyula Pauer's atlas. They usefully identify certain politicians as pro or anti-administration, much in the way that historians classify the factions in the US Congress during the Washington administration. Essentially, those members elected from occupied territory, or from areas with heavy slave populations, supported the Davis administration. Those from the back country, the hills and mountains without much in the way of human chattel, opposed many war measures. But those are generalizations.