[98] In 1958, Kennedy introduced a bill (S. 3974) which became the first major labor relations bill to pass either house since the Taft–Hartley Act of 1947. The bill dealt largely with the control of union abuses exposed by the McClellan committee but did not incorporate tough Taft–Hartley amendments requested by President Eisenhower. It survived Senate floor attempts to include Taft-Hartley amendments and gained passage but was rejected by the House.[99]
At the 1956 Democratic National Convention, Kennedy gave the nominating speech for the party's presidential nominee, Adlai Stevenson II.[100] Stevenson let the convention select the vice presidential nominee. Kennedy finished second in the balloting, losing to Senator Estes Kefauver of Tennessee but receiving national exposure as a result.[101]

Results of the 1958 U.S. Senate election in Massachusetts. Kennedy's margin of victory of 874,608 votes was the largest in Massachusetts political history.[102][103]
A matter demanding Kennedy's attention in the Senate was President Eisenhower's bill for the Civil Rights Act of 1957.[104] Kennedy cast a procedural vote against it and this was considered by some to be an appeasement of Southern Democratic opponents of the bill.