Actually, the two-thirds Cloture rule was adopted by the Senate on March 5th, 1917 at the urging of President Wilson. Before this date there was not way to cut off debate, so its adoption had nothing to do with the pre-Civil War period, it concerned issues of the WWI period.
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For a long time the Democrats required a two-thirds vote for a person to become the Presidential nominee--so that the Southern Democrats could block anyone they didn't like.