The U.S. colloquial phrase where the rubber meets the road, and variants, mean:
– where the important facts or realities lie;
– where theory is put into practice.

With one exception, all the texts containing the earliest occurrences of the phrase that I have found indicate that it originated in the jargon of the advertising business—jargon in which let’s get down (to) where the rubber meets the road meant how much is it going to cost?.

These are as the texts in question, in chronological order:

1-: From the column After Last Night, by Will Jones, published in the Minneapolis Morning Tribune (Minneapolis, Minnesota) of Monday 23^rd April 1956:

How to Talk like a man in a very dark gray flannel suit (a further round-up of Madison Avenuisms ¹):
“Let’s stop rooting around on the ground for acorns and look up and see where they’re coming from.”
“Let’s get down where the rubber meets the road.”
“We’re up against the hot pipes on this one.”
“Don’t let the boat get too far from shore or we may get our feet wet.”
“That’s the way the cookie crumbles.”
“Skim this over the pond and see if it reaches the other side.”
“Let the air out of it and see what you’ve got.”
“Let’s shake the tree and see how many apples we get.”
“Let’s smear it on the cat and see if she licks it off.”

¹ Madison Avenue is the name of a street in New York City, which is the centre of the U.S. advertising business; this name is used allusively to denote the U.S. advertising business and the U.S. advertising agents collectively.

2-: From the column In Hollywood, by Erskine Johnson, published in the Dixon Evening Telegraph (Dixon, Illinois) of Saturday 26^th May 1956:

It takes more than a gray flannel suit to be a succses [sic] in the advertising jungle of radio and TV. You gotta talk the language of the natives—a collection of stylized phrases that trademark advertising men from Madison Avenue to Hollywood and Vine.
The jargon gets a king-sized airing on the screen in a new movie, “The Great Man.” ² Keenan Wynn ³ plays a Madison Ave. genius with a gift of gab and of a language that Berlitz doesn’t teach. Some of his chatter:
To edit a TV script: “Let’s toss it on the floor and walk around it.”
To move quickly because of a deadline: “We’re too close to the green to use a five-iron.”
To see what the client thinks about it: “Let’s stop rooting around on the ground for acorns and look up to see where they’re coming from.”
How much is it going to cost?: “Let’s get down to where the rubber meets the road.”
Let’s try it out on the top brass: “Let’s run this one up a flagpole and see who salutes.”
Maybe it won’t work: “Don’t get the boat too far from shore or we’ll get our feet wet.”

² The Great Man (1956) is a U.S. film noir directed by and starring the Puerto Rican actor and theatre and film director José Ferrer (1912-1992).
³ Keenan Wynn (1916-1986) was a U.S. actor.

3-: From the column Cityside, by Gene Sherman, published in the Los Angeles Times (Los Angeles, California) of Thursday 18^th April 1957:

PATOIS—Being a sucker for ad agency jargon I was interested to learn Universal-International has put some together for “The Great Man.” The remarks in the picture include “Let’s toss it on the floor and walk around it,” “We’re too close to the green to use a 5-iron” and “Firm it up in one ball of putty.” Got Keenan Wynn so interested he dug up a few more, just for kicks: “Let’s stop rooting around on the ground for acorns and look up to see where they’re coming from,” “Let’s get down where the rubber meets the road,” “We’re looking for a real barnburner,” “Let’s anchor it in deep water overnight and see if it develops any leaks,” “Smear it on the cat and see if she licks it off,” “This is only woodshed research, so don’t follow it out the window,” “I’m throwing it out for grabs because it’s got a lot of glue on it,” “Let’s cross-pollinate on this,” “What have we got when we let the air out of the balloon?” “Run it up the flagpole and see who salutes,” “Skim it across the pond and see if it reaches the other side” and “We’ve got the motor running, but the mixture’s a little rich.” In the ad agencies, ma’am, that’s the way the banana peels.

4-: From the column Matter of Fact, by Al Osborne, published in the Binghamton Press (Binghamton, New York) of Friday 12^th July 1957:

Editor’s Note: Tom Cawley, regular conductor of Matter of Fact, is on vacation. During his absence, former staff writers of The Press are contributing guest columns on reminiscences of newspaper day in Binghamton. Today’s guest is Al Osborne, associated with a Buffalo advertising agency.
[…] The telephone rang.
[…] I answered it. […]
[…]
Cawley: Sorry to bother you old man.
Osborne: Always time for an old friend, Carl.
Cawley: Tom. Tell you what: going on vacation, old man. No one will write the column this year. Thought I’d ask Press alumni to contribute. Thought of you.
Osborne: Always happy to hear from an old friend, Bert.
Cawley: Tom. How’d you like to write one?
Osborne: One what?
Cawley: Column.
Osborne: Let me run that up the flagpole and see who salutes. […] In fact, let’s mentally skip that across the pond and see if it makes the other side.
Cawley: The column, old sport, would be what you remember about Binghamton.
Osborne: Now we’re getting down to where the rubber meets the road.

5-: From Hal Boyle’s ⁴ column, published in many U.S. newspapers on Wednesday 31^st July 1957—for example in The State Journal (Lansing, Michigan):

Right now greatest interest centers in two new weird and wonderful languages—one spoken by the teen-ager, the other by the man in the gray flannel suit.
This second language—now known as “businessman’s bebop”—originated in the ivory tower world of advertising has spread throughout all industry with the speed of chickenpox in a kindergarten.
Edward M. Meyers, a merchandising and sales promotion expert, has collected a number of these “gray flannelisms” overheard in conferences in many executives suites.
Here are a few, selected at random, for the young go-getter who wants to pep up his conference vocabulary:
“What this idea needs is more of an idea.”
“Let’s stick antlers on it and see if it scratches.”
“As long as the boss doesn’t have to do it nothing is impossible.”
“Let’s put it on a scale and see if it’s gained any weight.”
“Let’s get down to where the rubber meets the road.”
“It needs a transfusion and the account executive isn’t our blood type.”
“Let’s not just stand around with our backs against the hot pipes.”
“Let’s follow it down the road and see what it eats.”
“I don’t know about the rest of you, but I’m ready to pitch a tent and dig for worms.”
“Let’s drive it into the parking lot and see if we dent any fenders.”
“Let’s put on pith helmets and try running it around in the sun.”
“That’s the way the banana peels and the mop flops.”
“Let’s ignore it before we think about it.”
“Let’s try it with an accent and see if it’s subversive.”
“At this stage we’re chopping wood—not burning it.”
“Let’s throw a blanket on it and keep it warm.”
“Let’s not show it to him. He might cancel his vacation.”
“I’m just painting with a broad brush. You fellows fill in the details.”
“Let’s give it a name and see if someone will adopt it.”
“Let’s wash it and see if it shrinks.”
“He’s not interested in winners—he just wants to know if it can make the stable.”
“Let’s take it up the stairs and see if it wheezes.”
“Let’s not X-ray it. We might see it too clearly.”
“The drawbridge might be up—but you can still jump the moat.”
“Let’s anchor it in deep water and see if it develops any leaks.”
“Let’s frame it and see if it collects dust.”
“I’ve got the motor running, but I think the mixture is a little weak.”
“Let’s not bake any beans. I’ve got to catch the 5:27.”
“Let’s put it in a cage and see if it sings.”
“I see feathers on it—but it’s not flying yet.”
“Let’s get down on all fours and look at it with humility.”
“Let’s hang on to the tail. You can never tell where it will wag us.”
“Let’s forget it before we file it.”
Let’s!

⁴ Harold Vincent ‘Hal’ Boyle (1911-1974) was a U.S. journalist.

The only text containing an early occurrence of the phrase that is not explicitly associated with the jargon of the advertising business is this advertisement, published in the Shreveport Journal (Shreveport, Louisiana) of Monday 21^st January 1957:

THIS FACT gets down where the rubber meets the road:
“We Sell ’em Cheaper . . . ’cause We Always Sell More!”
Wray-Dickinson Co.
Ford
“Louisiana’s Oldest Ford Dealer”