This argument is used as part of the Southern Strategy, when Republicans/Right Wing took over the South.
Unfortunately, it is untrue on two levels: The Civil War was between a national government and a rebellious (treasonous) part of the country. It was not between the Northern states and the Southern states.
Second, the reason for the rebellion was specifically slavery.
From the South Carolina Declaration of Independence:
[Actions by the federal government]...fully justified this State in then withdrawing from the Federal Union; but in deference to the opinions and wishes of the other slaveholding States, she forbore at that time to exercise this right. Since that time, these encroachments have continued to increase, and further forbearance ceases to be a virtue.
And, the right of property in slaves was recognized by giving to free persons distinct political rights, by giving them the right to represent, and burthening them with direct taxes for three-fifths of their slaves; by authorizing the importation of slaves for twenty years; and by stipulating for the rendition of fugitives from labor.
http://avalon.law.yale.edu/19th_century/csa_scarsec.asp
From the Georgia Declaration:
For the last ten years we have had numerous and serious causes of complaint against our non-slave-holding confederate States with reference to the subject of African slavery.
http://www.civilwar.org/education/history/primarysources/declarationofcauses.html
The fact is that it is not politically palatable to admit an affection for slavery. So, a variety of other reasons have been invented (taxes, tariffs, etc.) to make modern voters swallow these lies, but the fact remains. The Civil War was fought because of slavery. To say otherwise is to fly in the face of the facts.