I hope you don't mind, but I moved your post to "A Cellar of Fine Vintages," our vintage deck forum.
You have a FINE specimen of a deck there. I can't tell in the photo, but judging from size the tax stamp compared to the deck, I'm guessing those are miniatures? I've only ever seen this deck design in poker size, and there was a reprint of the back made a few years ago by the U.S. Playing Card Company (USPC).
Squeezers was a popular term for cards with indices, back when the index was first developed. You could "squeeze" the cards together in your hand and still know what you were holding.
The back design itself has an interesting history. It pictures two bulldogs, "Trip" and "Squeezer" chained to their respective doghouses, with a moon smiling in the background and that quote, "There is a tie that binds us to our Homes." It's designed to commemorate a rather famous act of collusion between two companies! In the early days of the indexed playing card (which came about roughly in the 1870s), New York Consolidated Card Company had their "Squeezers" brand, with a letter and a suit symbol in the upper left corner when rotated either way, while A. Dougherty had their "Triplicates" brand, with miniature images of the entire card in the upper left corner when rotated either way. Rather than duke it out, fighting for market share, they colluded to split the market, with Squeezers dominating in one half of the country and Triplicates in the other. (I forget which had which, but based on the placement of the dogs in the image, I would guess "Trip" had the North, "Squeezer" had the South.) The date on Trip's doghouse, 1877, is the date the agreement was finalized.
It didn't last for very long, however - Russell Morgan Printing became the USPC in 1891, bought NYCC in 1894, bought Dougherty in 1907, merged the two into Consolidated Dougherty Co. in 1930 and absorbed them into the parent company in 1962.
Now, while your deck does say "The N.Y. Consolidated Card Co." on it, that's no guarantee that the deck was made while the company was still independent or at least an independent division of USPC. To this day, USPC still makes Tally Ho Playing Cards with the A. Dougherty brand name on them, despite the company no longer existing under that name for the past 85 years. The tax stamp makes me think it's not older than my estimate of early 1940s - but then again, I'm assuming it's a "1 Pack" stamp and not something else, because it's not fully intact. In fact, as I look closer, it could also be the "10 cents" wide stamp, in used from 1929 to 1940. The cancellation appears to say "C.D.C.", which would be Consolidated Dougherty, which existed from 1930 to 1962.
OK, gathering my thoughts and based on all this observation, I'd say you have a "Depression Era" deck, made between 1930-1940, assuming that's a 10 cents stamp. If it's a 1 Pack stamp, it's likely sometime in the early to middle 1940s at most - I don't think they were still packaging cards like this by the 1950s. Under no circumstances was the deck made later than 1962.