The New York Times has bet on digital subscriptions to play a central role in its long-term future. But while selling access to the paper’s Web and mobile versions was an initial hit, growth is slowing — and may stop altogether if the company’s earlier projections are correct.

Four years ago, before the Times put up a paywall around its then-free site, the paper asked consulting firm McKinsey & Co. to estimate how many digital-only subscriptions it could sell. The conclusion, according to people who have reviewed the study: In the most optimistic case, just under 1 million subscribers would pay $15 to $30 a month for access to the New York Times website and app. More likely, however, the theoretical limit at these prices would be 800,000 to 900,000 subscribers.

The problem is, the Times already hit the low end of that projection in June with 831,000 paying online readers. And the number of new customers it added in the three months leading up to that point, about 32,000, were mostly for the new NYT Now app, a slimmed-down version of the Times that costs $8 a month. It looks like the McKinsey study got it right.

There could be some cannibalization from the new app, of course, but even if all 32,000 were for the main digital subscription (which costs $15 to $35 depending on how many devices you want to use), that would still fall short of the previous two quarters when the Times averaged 36,000 new subscribers.

Paywalls are important because of how quickly they’ve become the main (or only) strategy for a lot of U.S. newspapers as advertising deteriorates. About four in 10 papers in the U.S. charge online, and it’s likely to only increase. In the case of the Times, the paywall is now a significant part of its total business, accounting for a tenth of annual sales.

And it’s all new money for the Times, about $149.1 million last year, a palpable performance in a short period of time. Put it another way, in a little over two-and-a-half years, the paywall went from $0 to $150 million.

But a slowdown in digital subscribers means it’ll be that much harder for the Times to make up for its losses elsewhere, specifically in advertising, once the life-blood of the business. The company lost close to $90 million in ad revenue — print and online together — from 2011 through last year, and it has been on a downward track ever since.

Online revenue alone would not sustain the New York Times as it exists today. If the Times were to become a digital-only newsroom, it’d be a $312 million business, including the $162.9 million in online ads it generated last year. But that’s only 20 percent of its current sales. In other words, a digital-only Times could just support a fifth of its current newsroom, or around 200 journalists.

It’s worth noting that the Times was the first general-interest publication to charge for online access. While it followed in the footsteps of the Wall Street Journal and the Financial Times, which created the metered model the Times adopted for its own paywall, it broke new ground. It wasn’t clear if anyone would bother paying for general news online.

“They deserve a lot of credit for that,” said Ken Doctor, a media analyst at Outsell. Doctor independently analyzed the Times’s addressable market for online subscriptions and arrived at roughly the same figures as the confidential McKinsey study.

New Apps, Lower Cost

The Times declined to comment on the McKinsey study, but the company referred to comments CEO Mark Thompson made at an investor conference in May: “It’s not ridiculous to think of a high single million number in the U.S. as an addressable market.”

Translation: We think we can sell 8 million or 9 million subscriptions — eight or nine times where we’re at now — at a variety of price points, but likely with the bulk of growth at lower than current price points.

The McKinsey study did show that lower-priced subscriptions could draw in millions of customers. At a half-inch thick, the report included an exhaustive market analysis showing how many readers the Times could draw at different retail costs, a standard price elasticity survey, according to one insider. The Times hasn’t run a similarly exhaustive study since, this person said, though it has more recently run a series of smaller market studies leading up to the launch of NYT Now.

More than a year ago, company executives — including Thompson, publisher Arthur Sulzberger Jr and Denise Warren, who leads the Times’ digital products division — anticipated the Times would soon reach the ceiling of subscribers predicted by the original study and aggressively pursued the creation of new apps to spur growth, one of our sources said.

That led to NYT Now and also NYT Opinion, a collection of its daily commentary and columns for $6 a month. A food app will be available this Fall.

The new apps helped the Times add 32,000 paying online readers in the second quarter, but Doctor estimated about 20,000 of those were for NYT Now, which he calls, “subpar and below expectations.”

Warren acknowledged that the Times’s marketing strategy around the new apps didn’t work. “We need more precision to determine which is the right customer for the right offer,” she said on a conference call with analysts following its earnings report at the end of July.

The idea of charging for content wasn’t just a flash point among outside observers. There were plenty of people inside Times headquarters who were either outright against the proposition or weren’t entirely sure of its merits, according to several people who preferred to remain anonymous.

But at least one Times person had publicly touted the benefits of online subscriptions: Former executive editor Jill Abramson, who was unceremoniously ousted in May. Just a month before her exit, she hosted a gaggle of media reporters at a cocktail reception on the 15th floor of the Times building to talk about its new digital subscription products.

“I believe that a lot of the people who are gonna subscribe to NYT Now are going to become hopelessly addicted,” she said to the gathered, as Sulzberger and Thompson looked on.

We’ll get a chance on September 4 to see if Abramson’s views have changed, when she sits down for a chat with Re/code’s Kara Swisher at our next Code/Media conference in New York. It’ll be her first onstage interview since leaving the Times.