Slavery was the specific issue... however it was on the way out anyways. In order to secure the European support necessary for their long term independence, the Confederates would have had to at least formally emancipate their slaves sooner or later.
And I would argue that there is no way that the South would have been able to mobilize the degree of support among its people that it did if it had presented the cause as a right to keep the slaves (just like the Union population would have dropped out of the war in short order if Lincoln has said that the main reason for fighting was to free the slaves). Lets face it, the vast majority of Southerners were fighting against a government that they thought no longer represented them... they didn't own slaves, nor were they dependent upon them... and while slavery was a big issue when it came to secession it wasn't the cause that the Southerners were fighting for.