“That dog won’t hunt” (LBJ)

President Lyndon B. Johnson said “that dog won’t hunt” in the 1960s. The ultimate origin of the phrase (used since at least the 1930s) is unknown, but LBJ certainly popularized it. The phrase was made into a song by Waylon Jennings in 1986.
 
“That dog won’t hunt” means that a person or idea is not good and isn’t going to work out.
 
   
Bye Bye Texan-ese
by L. E. Guillot
Dallas, Texas (published by author)
1962
Pg. 29: 
That ole dog won’t hunt.
   
Waylon Jennings lyrics
That Dog Won’t Hunt 
(Written by R. Murrah / J. Schweers)

Well, you think that you can lie and tell me alibis
And it’s alright
Keep the grapevine line working overtime
On your late nights.

You think you can say some words,take away the hurt
And I’ll still be your number one
But when it ain’t working out we got a saying down South
Baby, that dog won’t hunt.

Chorus:
Baby, that dog won’t hunt
So you can hang up your guns
Break my heart and then you want a new start
Baby, that dog won’t hunt.
 
Google Books 
You All Spoken Here
by Roy Wilder, Jr.
Athens, GA: University of George Press
1998
Pg. 57:
That dog won’t hunt, that cock won’t fight:
The hell you say; it ain’t practical; my hind foot; you’re trying to sell me a bill of goods.
 
(Dictionary of American Regional English)
dog won’t hunt, that phr. Also that cock won’t fight
That won’t succeed.
1933 Williamson Woods Colt 148 Ozarks, That feller is jest naturally a fool for the lack of sense, a-tryin’ to mix whiskey an’ lyin’. He ort t’ of knowed that dog won’t hunt!
 
December 1939, American Speech, “Folk ‘Sayings’ from Indiana” by Paul Brewster, pg. 266:
“That old dog won’t hunt,” meaning that an excuse offered will not serve.
 
7 February 1970, Charleston (WV) Gazette, pg. 5:
He (President Lyndon B. Johnson, in 1968—ed.) then asked Ambassador Ellsworth Bunker in Saigon for his recommendations on the proposals by Goldberg and Rusk.

On the Goldberg proposal to stop all the bombing, Bunker “came back strong and said, ‘I just can’t. That dog won’t hunt. We just cannot get that over, it would just blow everything.’”
 
4 December 1970, Newark (OH) Advocate, “Taking the semicolon off” by John P. Roche, pg. 4:
“Now he tried that in ‘66, and I told him that dog won’t hunt. Why can’t he learn?” (Referring to a typical Lyndon Johnson speech—ed.)
 
4 December 1971, Charleston (WV) Gazette, “Democrats Ponder the Blame Game” by Tom Wicker, pg. 5:
This is a splendid example of O’Brien’s Irish gift for Irish Blarney, and a pretty good political try, but as Lyndon Johnson used to say, “That dog won’t hunt.”
 
30 October 1981, Frederick (MD) News, “Washington has a word for it” by James Carey, pg. A6:
Lyndon Johnson, too, is recalled as a man who always “mashed” buttons instead of pushing them, and who sprinkled his conversation with rural expressions like, “That dog won’t hunt”—meaning a proposed solution wouldn’t work.
 
6 August 1987, New York Times, pg. A27:
That Dog Won’t Hunt
“In the Nation” by Tom Wicker
   
December 1991, PS: Political Science & Politics, “Doing ‘Tuesday Lunch’ at Lyndon Johnson’s White House” by David M. Barrett, pg. 678:
When North Vietnam insisted in a statement that the U.S. stop all bombing, but refused to pledge reciprocal actions, Johnson dismissed the message with traditional Texas shorthand: “That old dog won’t hunt” (April 25, 1968:1).
 
30 May 1999, New York Times, pg. BU6:
However You Train It, That Dog Won’t Hunt