Typically used of something that comes to an end, the phrase not with a bang but a whimper means in an anti-climactic, disappointing way. The variant with a bang and not a whimper means the opposite.

A variant of this phrase occurs, for example, in the concluding paragraph of Go out with a bang, an editorial about Jim Kenney (born 1958), Mayor of Philadelphia, published in The Philadelphia Inquirer (Philadelphia, Pennsylvania, USA) of Sunday 13^th August 2023:

This should be an all-hands-on-deck effort. For Kenney, it could reshape his legacy as the mayor who helped save democracy. He could go out with a bang instead of a whimper.

The phrase not with a bang but a whimper alludes to the last line of The Hollow Men, published in Poems 1909—1925 (London: Faber & Gwyer Ltd, 1925), by the U.S.-born British poet, playwright and critic T. S. Eliot (Thomas Stearns Eliot – 1888-1965):

This is the way the world ends
This is the way the world ends
This is the way the world ends
Not with a bang but a whimper.

The earliest occurrences that I have found of the phrase not with a bang but a whimper and variants used without explicit reference—or with only passing reference—to T. S. Eliot’s poem are as follows, in chronological order:

1-: From The Colonel’s Daughter (New York: Doubleday, Doran & Company, Inc., 1931), by the British poet, novelist, critic and biographer Richard Aldington (born Edward Godfree Aldington – 1892-1962):

‘There are two sorts of traitors to humanity I particularly dislike. The first are the smug bastards who declare that all is for the best in this best of all possible worlds and pray that our unexampled prosperity may last. The second are the peeving cynics like you, who say nothing ’s worth while, human nature ’ll never change, the sooner it ’s all over the better. I wish you ’d all shoot yourselves with a bang, instead of continuing to whimper.’

2-: From If the Indian Conference Fails, published in The Manchester Guardian (Manchester, Lancashire, England) of Monday 9^th November 1931:

What enthusiasm was carried over from the first session of the Conference is now largely evaporated. […] The Conference gives every indication of going out—as Mr. Eliot puts it—“not with a bang but a whimper.”

3-: From The Years of the Locust (America, 1929—1932) (Boston: Little, Brown & Company, 1933), by the U.S. author Gilbert Seldes (1893-1970):

The birth rate fell in 1931 seventeen per cent. below the rate of 1921, ten per cent. lower than that of 1926. If the next hundred years are to mark the slow decline or the catastrophic disappearance of our civilization, going out with a bang or a whimper, at least there will be fewer human beings alive to enjoy the spectacle.

4-: From From A Window In Fleet Street, A. D. Emmart’s column from the London Bureau of The Sun, published in The Sunday Sun (Baltimore, Maryland, USA) of Sunday 9^th July 1933—the following is about the World Monetary and Economic Conference:

“Tower of Babel” was used a lot because some correspondents were vastly impressed, or pretended that they were, at the assembling of representatives of sixty-six nations, even though there was no real confusion of languages since all of the delegates seem to understand either French or English. Maybe there was something subtler in the phrase, “the tower of Babel went crashing.” But the conference isn’t likely to do that. If it has a sad end it will be much more like the kind of finish that T. S. Eliot ascribes to the world, coming “not with a bang but a whimper.”

5-: From a letter to the Editor, by one Nazar Mohamad, of Lahore, published in The Civil & Military Gazette (Lahore, Punjab, Pakistan) of Sunday 23^rd July 1933:

The Muslim League has outlived its usefulness. The League is not capable of giving a lead to the country on any issue. All it has done lately is to give a display of its spirit. There is no aim or purpose for this body which is being pursued by its protagonists. The ideals and methods of the Muslim League are so stereotyped and well-worn that they fail to inspire the public. In fact the Muslim League is moribund, and so let it “end not with a bang, but a whimper.”

6-: From the review of Creative America (New York: Harper & Brothers, 1933), by the U.S. novelist and literary critic Ludwig Lewisohn (1882-1955)—review by Harrison C. Coffin, published in The Evening Sun (Baltimore, Maryland, USA) of Saturday 2^nd December 1933:

The work of 120 American writers appears here. Many of the selections will be familiar to anyone who has had a good old-fashioned common school education, especially if that education was enjoyed in New England, if enjoy is not too brave a word to use in connection with New England education. The first selection is by William Bradford, and from there we go on through the whole pageant, through the work of polite poets, troubled romancers, critics, essayists, and what not, ending—not with a bang but a whimper—with one of Hart Crane’s impenetrable poems.