Dan, in his history of the upper chamber, The Senate: 1789-1989, Senator Byrd details why President Truman wanted to keep the majority leader out of the line of succession:

There may also have been an institutional factor in Truman’s reversal of the roles (putting the House speaker before the president pro tempore). Between the 1886 removal of the president pro tempore from the order of succession and 1947, some entirely new leadership posts had evolved in the Senate: the majority and minority leaders and the party whips. . . By 1945, most Washington observers regarded the majority leader as the Senate’s functional equivalent of the Speaker of the House of Representatives, while the president pro tempore had become more of a ceremonial office. Had Truman drawn a list of men, rather than offices, he would certainly have included Alben Barkley (the majority leader) in the line of succession — indeed, in 1948, Truman chose Senator Barkley as his vice presidential running mate. But, for the purposes of legislation, the president recommended inclusion of a constitutionally created office, the president pro tempore, rather than a party-designated officer, the majority leader.