One early form of this expression in U.S. English, not intended to be taken literally, is "Do me a favor and drop dead." A Google Books search finds examples of this phrase from as early as 1940, in a snippet from The New Yorker:
Then, full of enthusiasm and big talk, he buys a couple of fifty-cent cigars and goes to Ganger's ofiice and asks him to decorate and furnish the joint. "Here, Arthur," he says, "have a cigar." At first Ganger is hostile. "Get out of my sight," he says. "Do me a favor and drop dead." If the promoter, outraged by this treatment, begins shouting, Ganger holds up both hands, palms out. "Don't pressure me," he says wearily. "Anything you might tell me, I heard it all before."
Also, from Robert Mende, Spit and the Stars (1949) [combined snippets]:
"Huh?" asked Gregg not paying attention to the question. He was watching Dynamite walking further and further away. If I run, he thought, I can catch up with her. Yeah, but if Mrs. Gross sees me running after a girl, the whole block will know about it. "Oh, Mrs. Gross," muttered Gregg, "do me a favor and drop dead."
"What did you say, Gregg?"
"Er . . . er . . . dumb head. I got a dumb head it takes me a long time to study words."
Evidently, Mende's novel was reissued in 1956 as Tough Kid from Brooklyn.
And from Congressional Record: Proceedings and Debates of the ... Congress (1954) [quoted snippet not shown in snippet window]:
Senator Fulbright, Senate Office Building, Washington, D.C.
Dear Senator: Would you please do our country a big favor and drop dead? McCARTHY is an American. What are you?
A. Rawson. New York, N.Y., November 23, 1954.
Fred Kogos, Dictionary of Yiddish Slang and Idioms (1967) lists the Yiddish version of "Do me a favor and drop dead" as an idiom/slang expression in that language:
Folg mich a gang un gai in drerd! Do me a favor and drop dead!
It thus seems possible that this early ironic (and nonliteral) request for a particular favor is a direct translation of a longstanding Yiddish expression into English. Early instances of the expression seem to have a New York City nexus, but this fact may offer only very weak circumstantial evidence of Yiddish influence in the emergence of "Do me a favor and drop dead" as a familiar expression across much of the United States.