You are missing the point entirely. American abolitionism between roughly 1840 and 1861 had essentially two schools of thought to it. One said that the constitution was a doctrine of freedom. The other said that the constitution was a doctrine of slavery. Spooner's camp was the first. Garrison's was the second. Amidsts all the internal debates over the nature of the US Government and its constitution between these two camps, virtually all abolitionists eventually came down on one side or the other. The anti-constitutionists attracted their own following and other prominent abolitionists such as Phillips. The constitution supporters attracted a following as well, specifically the Liberty Party, Gerrit Smith, and Frederick Douglass.
So where did Spooner fit into that dispute? Simple. His book, The Unconstitutionality of Slavery, was the defining articulation of the constitutional abolitionists argument - the book around which they based their school of thought. Spooner is, quite simply, to the concept of constitutional abolitionism what Blackstone is to the concept of common law.
FURTHER, it should be noted that when the pro-slavery forces looked out and saw their opponent's arguments they effectively saw these two schools in the abolitionist field. When they saw these two schools they believed that constitutional abolitionism was a substantially stronger argument than other school's anti-constitutional views. That is what Senator Brown effectively conceded. Anti-constitutional abolitionism was rabble oriented and by necessity of its beliefs demanded the complete overhaul of the U.S. Constitution. Garrison called that Constitution a "pact with the devil" and wanted to be rid of it. He wanted to invalidate it, tear it to shreds, burn it, and replace it with something entirely different. Contrast that with Spooner's position, which not only rejected the notion that the Constitution would have to be rewritten but turned to that document itself as an instrument of freedom. Garrison saw the constitution as a roadblock to abolition. Spooner saw the constitution as a tool of abolition.
It's you contention that his arguement provoked anything in the South other than book burnings that's out of place.
I know of no recorded event in which the said burnings of Spooner's book took place. I do however know that hundreds of copies of it were provided free of charge to southern government officials and, by all accounts, they kept them and read them as Senator Brown said. Rabbles burn books that argue against their viewpoint, Silas. Intelligent men read them even if they are arguing against their viewpoint. They do so to determine if there is merit to that argument and see just how strong or weak it is.
The South did contend that the Abolition of Slavery was cause for secession
Your wording is imprecise and accordingly leads you to a false conclusion. The south asserted a particular brand of abolitionism to be a cause for secession, viz.: the people like John Brown who were waging domestic terrorism on civilians and inciting slave rebellions. They also asserted that the restriction of slavery from the territories was a cause for secession. The liklihood that slavery itself would be immediately abolished outright and in full was not a possibility in 1861 though, and thus not a cause for secession.