Early occurrences of 'choked up' and 'choked' in baseball settings
In the context of sports, use of choke to mean "blow an easy opportunity" seems to go back to baseball in the years shortly after World War II. The Random House Historical Dictionary of American Slang (1994): has this entry as one of its definitions of choke:
choke v ... 2. Esp. Sports to become tense or lose one's composure in a critical situation.Also choke up.
The dictionary then offers an example from Bill Roeder, Jackie Robinson (1950):
In one of the vital pennant battles in St. Louis, Robinson grabbed at his throat to signify that Bill Stewart, the umpire, was "choking up." Stewart threw him out of the game.
A second early example from baseball (also cited in the Random Hose dictionary) is from Jim Brosnan, Pennant Race (1962). Here's how Brosnan describes the scene in early June 1961 at his hotel home (during baseball season) in Cincinnati a few hours after he had blown a late lead for the Reds and lost a game to the Cubs:
The doorman didn't notice me slinking into the foyer. He was working a patron who'd checked out of the hotel, and said, "The Reds really choked again today. That puts the Dodgers in first. They'll never win the pennant."
I didn't even eat dinner that night.
These examples—particularly the Jackie Robinson one—suggest that early users of the slang term choked really did equate failing under pressure with losing the ability to breathe and to function normally, and thus with failing to maintain one's composure and to perform well.
I should perhaps add that "choking up" as Jackie Robinson used the term has nothing to do with "choking up" in the sense of gripping a bat one or more inches above the knob of the bat. In the latter case, the thin part of the bat handle is imagined as the neck of the bat (the widest part of the bat is called its head), so "choking up on the bat" means gripping the bat slightly closer to the head, which, done within reason, can help improve one's bat control at the cost of some loss in power.
Early occurrence of 'choke in the clutch'
A Google Books search finds an instance of "choke in the clutch" in Paul Krassner's The Realist, issues 71–98 (1968–1974) [combined snippets]:
23 July 1968
It was during Indian batting practice that I first actively participated in don Don's cryptically esoteric hallucinatory religious ceremony, or he called it, his "little pre-game show." I was taking extremely careful notes regarding don Don's concoction:
There were several small pieces of rosin from the pitcher's mound, three one-inch squares of pine tar rag, a scratched recording of the Star Spangled Banner sung by Eddie Fisher and Mel Ott, two hot dogs with French's mustard (a creamy yellowish substance) and two beers. Don Don said that the mustard was not essential but that it did make the recording more palatable.
I told don Don that I was terribly afraid, that I had never experienced anything like this before and that my mother expected me home for dinner after the game. He said not to be afraid since the Great Team Spirit would protect me and that by the bottom of the fourth we would be well on our way to the land of the Grand Slam and the Perfect Game. So knowing that you don't walk a guy intentionally with the bases loaded, we proceeded to ingest a mixture of all the ingredients.
"I am pleased that you did not choke in the clutch," don Don said.
This article was probably published in 1968 or soon thereafter. The story appears to be a burlesque of Carlos Castañeda's The Teachings of Don Juan: A Yaqui Way of Knowledge, (which was published in 1968), and the diary entries that make up the story include dates from July and August 1968. On the other hand, the version in Google Books is presented in snippet-view format, and it appears in a collection of issues of The Realist stretching from 1968 (issue 71) to February 1974 (issue 98), so its precise publication isn't clear from the Google Books data.