In one of the latter years of my undergraduate program I read/heard from one of my classes that discussing the slave trade/slavery on either the Senate and/or House floor (I forget which) was banned. Is this true and if so, how could I confirm it?
I believe this is referring to the gag rule (aka: Pickney Resolution 3) of the US House, adopted in 1836. It read:
As background, realize that an important but often-overlooked part of the First Ammendment is the right to petition the government.
Congress had been receiving a lot of petitions from US citizens requesting slavery be somehow curtailed or abolished. This made Southern Congressmen rather irate, so they passed the above rule. In plain English, any slavery petition from any constituent would be automatically ignored.
While this might have done wonders to re-elect the Southern reps that put it forward, it incensed northerners (even ones that didn't care much about slavery). The way they saw it, there was no longer any real right to petition Congress on this particular matter, regardless of what the First Ammendment said. The number of such petitions just increased, and the southern-based Democratic party lost the next major election (1840).
If this kind of folly; the mass destruction of a party's image by its own politicians for individual short-term political gain; looks familiar, it should. Rather than take 1840 as a wake-up call, Southern Democrats only escalated this kind of behavior, culminating in Bleeding Kansas, the barbaric beating of Senator Sumner on the Senate floor, and ultimately The Civil War.
I'm familiar with the story, but it is a highly suspect claim. It is part of the Myth of the Lost Cause. The idea here is that compromise was impossible so war was the only option. For this reason, many sources may be unreliable and it would be best to use only primary sources to prove or disprove its veracity.
James Henry Hammond made his famous speech "On the Admission of Kansas" to the Senate in 1858. From this speech, we get the phrase "Cotton is King." He says, for instance:
The Corwin Amendment was proposed in 1861 by the House Republicans. This amendment would have made slavery legal permanently in the US, so the House had to have been discussing slavery.
According to Wikipedia
You could query the Senate Historical Office to find out if any procedural rule ever existed if you wanted to confirm it.
There is a book on the gag rule and John Quincy Adams' multiyear struggle to overturn it (I read the book and it's a good read...): Arguing about Slavery: John Quincy Adams and the Great Battle in the United States Congress (auth. William Miller, 1995).