Why did Harry Truman go without a vice president during his first term?

It wouldn't be until the passage of the 25th Amendment to the United States Constitution in 1967 that the President would be able to choose a replacement in the event of the vice presidency position becoming vacant.
After just 82 days in the role, Truman had had to vacate the vice presidency in the wake of President Roosevelt's death. Truman was a firm believer in the old order of succession established under George Washington, which he brought up to date by signing the Presidential Succession Act of 1947. Under this legislation, the Speaker of the House of Representatives would be placed next in the line of succession after the president of the United States, and ahead of the president of the Senate pro tempore. Critics accused Truman of playing politics with the succession, as it was widely known that he was much closer politically and personally to Sam Rayburn, the House Speaker, than he was to Kenneth McKellar, president of the US Senate pro tempore.