Q: Did Churchill say this?
(Updated from 2014.) “I contend that for a nation to try to tax itself into prosperity is like a man standing in a bucket and trying to lift himself up by the handle.” Did Churchill say this? Can’t find it in your Churchill by Himself (aka Churchill in His Own Words.  —A.R., New York City
Indeed he did—and he liked that “bucket” gag so much that he used it at least five times. The first appearances are in Robert Rhodes James, ed., Winston S. Churchill: His Complete Speeches 1897-1963 (New York, Bowker, 1974, 8 vols.)…
It is the theory of the Protectionist (tariffs advocate) that imports are an evil. He thinks that if you shut out the foreign imported manufactured goods you will make these goods yourselves, in addition to the goods which you make now, including those goods which we make to exchange for the foreign goods that come in. If a man can believe that he can believe anything. (Laughter.) We Free-traders say it is not true. To think you can make a man richer by putting on a tax is like a man thinking that he can stand in a bucket and lift himself up by the handle. (Laughter and cheers.) —Free Trade Hall, Manchester, 19 February 1904, Complete Speeches I: 261 
To all questions and complaints his Majesty’s Ministers have a single answer, ‘Send us back to office for seven more years,’ they cry, ‘and we will shut out the foreign devils and the goods the foreign devils make.’ What a programme for the 20th century! What an appeal to a civilized nation! …. (Loud cheers.) I am proud of the part I took in opposing the Government, that a country which tries to tax itself into prosperity is like a man standing in a bucket and endeavouring to lift himself up by the handle. (Loud laughter.) —Town Hall, Malmesbury, 18 December 1904, Complete Speeches I: 398. 
Retreading on Tax
This was too good a line not to remember for future use (he was good at that). But the editor in Churchill couldn’t resist improving it:
The doctrines that by keeping out foreign goods more wealth, and consequently more employment, will be created at home, are either true or they are not true. We contend that they are not true. We contend that for a nation to try to tax itself into prosperity is like a man standing in a bucket and trying to lift himself up by the handle. —Why I am a Free Trader (London: 1905); reprinted in Stead, Coming Men on Coming Questions (1905); and Michael Wolff, ed., The Collected Essays of Sir Winston Churchill (London: Library of Imperial History, 1975, 4 vols.) II 23.
In 1906 Churchill published For Free Trade (London: Arthur Humphreys, 1906; Sacramento: Churchilliana Co., 1977, 68). This contains the wording above, in which a few superfluous commas were edited out.
Endnotes: “Loud and sustained applause…”
(1) The “bucket” quotation reported in my first edition of Churchill by Himself was paraphrased. The version above (from For Free Trade) replaced it in the third edition, Churchill in His Own Words, and fourth edition Rosetta e-book. The fifth edition greatly expanded with 1100 new quotations, is in preparation for 2024. It will be published by Rosetta Books, Easton Press and the Hillsdale College Press. The tentative title is: Churchill by Himself: An Encyclopedia of his Greatest Words.
(2) Reactions of the audience, such as “(laughter and cheers),” are from transcriptions of original newspaper reports. Once when he thought they were lacking in one of his own volumes, Churchill inserted: “(loud and sustained applause).”
(3) The Complete Speeches version used the phrase “Aliens Government,” which I suspect is a typo; there was an Aliens Bill but not an Aliens Government; I have chosen to drop “Aliens” from the reported quote.