You can readily pick out the WatchTower's interest in this bill:
One of the several measures introduced in the Fifty-seventh Congress by right-wing senators seeking to retaliate against the Supreme Court for decisions protecting the constitutional rights of persons charged with subversive activities (see Subversion). One provision would have restored full investigative authority to congressional committees, which had been subjected to some limitations by the Court's 1957 decision in Watkins v. United States (see Congressional Power of Investigation). Another section would have restored full enforceability of state sedition laws, which had been limited in Pennsylvania v. Nelson (1956). A third would have rehabilitated the Smith Act, which made advocating overthrow of the government unlawful. This statute had been narrowly interpreted by the Court in Yates v. United States (1957).
The most serious constitutional issue posed by the Jenner-Butler bill, however, was its assertion of congressional authority over the appellate jurisdiction of the Supreme Court. The bill specified five areas where the Court's rulings had been challenged by conservative legislators and would have barred the Court from accepting or deciding such cases in the future. Arguably, constitutional support for such power may be found in Article III, section 2 of the Constitution and in a post–Civil War decision, Ex parte McCardle (1869).
Any such limits on the Court's appellate jurisdiction, however, would have severely challenged the Court's independent status, and the Senate was reluctant to subordinate the Court's appellate jurisdiction to control by Congress. Under the astute management of the Senate majority leader, Lyndon Johnson, all provisions of the bill were defeated, by a vote of 49 to 41, on 20 August 1958.
See also Appellate Jurisdiction; Communism and Cold War; Reversals of Court Decisions by Congress.
— C. Herman Pritchett
Read more: http://www.answers.com/topic/jenner-butler-bill#ixzz1ScIhIGoa
And a link to a Time Magazine article on the bill: http://www.time.com/time/magazine/article/0,9171,863386,00.html