Hard to estimate, I think, and depends on the definition. What about people that would play if they had access to a table but there is none? People won't put time into a game if they know they're the only person in 500 miles that plays it.
The short answer, I'd say, is to create a list of all carom tables in the U.S. I have reason to believe there are more carom tables than snooker tables.
I know, have seen, or must assume that I've run into about 50 carom players in Boston and southern New Hampshire.
World Class Billiards in Peabody has three tables. Tom McGonagle or McChen could give you a better idea of the number of players at World Class. Mazin Shooni's room is farther north near Manchester, NH, and I'd guess there must be a few dozen players in the area who play 3C.
The Boston metro area + southern New Hampshire accounts for more than 5 million people. I'm confident my count of 50 players is quite low. All the same, let's take the estimate of 10 carom players per million (10 CPPM).
The population in Maryland was about 4.5 million people in 1985. For 75 players, that's about 17 CPPM.
L.A. has a population of about 10 million. Given Bob's estimate of 3,000 players, that's 300 CPPM.
Given these estimates of 10, 17, and 300 CPPM and a U.S. population of about 310 million, the numbers based on Boston, Maryland, and L.A. numbers are
10 CP/million * 310 million = 3,100 carom players
17 CP/million * 310 million = 5,270
300 CP/million * 310 million = 93,000
Without grabbing any books on statistics, defining exactly what a 3C player is, etc., I'll take a wild swing without further justification and say the true number is about
10,000 - 30,000 carom players in the U.S.
or a few hundred carom players per state, on average.
I own a carom cue and Hoppe's book. I only play 3C once or twice a year, though I "practice" 3C on pool and snooker tables. I'd join the USBA, but for that small fee I could pay for my annual 3C table time. I'm not any good at carom and don't expect to improve much until I have room for my own carom table (in my thirty-room house on the Rock Candy Mountain in West Utopiaville). That or I can try to convince my wife that I need to go to Peabody every Thursday night to pick up groceries.
Would I count as a carom player?