As Obi-Wan Kenobi witnessed, the Kaminoan cloning project was essentially automated, requiring little intervention or inspection. Clones far outnumbered Kaminoans, even in the public showroom areas. They grow and train in an artificial environment, largely free of outside contact. Even their childhood instruction is computer-based. Clone production is therefore unlimited by labour costs, and Kamino's intake of raw materials can last as long as the Galactic Republic's credit on whatever accounts Sifo Dyas used.
Thus, like Separatist droid factories, the Kaminoan facilities are operable as a system of von Neumann machines: automated assemblers that continuously copy themselves whilst building the main product. The inexorable mathematics of the growth is the same, but the direct product is cloning facilities; the clones themselves are a byproduct expanding at comparable rates. Such an industry can double its scale in short times, growing until it impinges on the greater galactic economy. Self-sustaining, droid-based manufacturing spreads exponentially, like bacteria. For illustration: if the assemblers achieve a modest doubling time of 5 days, then a nursery that initially gestates 1000 clones per month would expand to a capacity of ~32000 in the next term, and over a million in the subsequent month. Computerised clone creches and schooling facilities must expand at a corresponding pace. Although the Kamino may have a 10-year lag-time to raise each individual clone, the concurrent batches expand as the production system naturally does. Hardware doubling in year zero yields effortless, delayed clone doubling in year 10. Each successive period's graduates can outnumber the previous batch by orders of magnitude.
Whether it happened fortuitously or by conspiracy, Kenobi discovered and inspected Kamino's growing clone army at the moment when “the first batallions [were] ready” [Taun We, AOTC]. This may seem like a galactically insignificant number, but it need only represent the first output from a production programme that was set into exponential acceleration a decade earlier. References to the size of this initial, demonstration batch are vague, but there is a firmly established lower limit on the numbers qualifying during Kenobi's tour:
The first batch of clone divisions are ready for deployment; millions more are undergoing intensive performance evaluations. [ITW:AOTC, p.21]
By definition, a division is on the order of ten or twenty thousand soldiers. When the Clone Wars erupted, Kamino was imminently ready to unleash millions of divisions of adult clones, presumably with ever larger, expanding ranks of younger clones following in later.
Some writers and commentators have badly misunderstood the crucial caption from Inside the Worlds of Star Wars: Attack of the Clones:
The first batch of clone divisions are ready for deployment; millions more are undergoing intensive performance evaluations. [ITW:AOTC, p.21]
This says millions of divisions, not millions of individual clones. This particular statement was completely deliberate: thoroughly researched and discussed when the text was drafted. Those involved were Simon Beecroft and John Kelly (writing and editing for DK Publishing), and Curtis Saxton (their consultant for technical accuracy); Jonathan Rinzler approved for Lucasfilm.
We knew that the Clone Wars were infamous on a galactic scale: widespread and convulsive enough to excite a farmboy on remote Tatooine a generation later. The war was remembered even where the existence of Jedi was forgotten. Mere millions of troops are insufficient to hold territory and fight a global war (like World War II) let alone a war across thousands or millions of worlds. In ITW:AOTC we purposefully kept the total figure open at the top end: the final Grand Army could be orders of magnitude bigger than the first millions of divisions. A smaller number would risk contradicting later tales of the Clone Wars, or would preemptively stunt the works of future writers. This caution has been vindicated by the lavishly scaled battles in dozens of star systems — particularly the grand scope of the Clone Wars cartoons and ROTS movie — which imply clone troops, and casualties, numbering far beyond a mere few millions. Yet the evidence of AOTC, such as the parade on Coruscant, had already undermined the “million clone” myth.
Why do some commentators continue to push the fallacious, irrationalist, ultra-minimalist view? The reasons probably differ between individuals. Discalculia and innumeracy. Failure to comprehend the scope of war, on either regional, terrestrial scales or the vaster stage of a galactic civilisation. Blind, misplaced, but good-intentioned adherence to older misinterpretations, which accumulate and grow as the spin-off literature moves further and further from the movies. Perhaps in some cases it's true disingenuity and recalcitrant opposition to Reason itself? Malign postmodernism and sophistry. Stubborn refusal to admit corporate or individual error? Buck-passing? A perverted love of perpetual discourse that avoids constructive outcomes? Vain insulation behind the personality-cults of online fandom?
Are the recalcitrants really worth debating? ITW:AOTC is a primary canon source (directly tied to a movie). As such, it outranks the more remote, spin-off “expanded universe” sources. If a fan magazine or peripheral novel tries to downscale the clone army to something smaller than the British Empire's or Soviet Union's, then it is wrong on that particular point. While a few secondary sources do perpetuate this mistake, they are overwhelmed by the weight of specific visual and circumstantial evidence showing the vast, breathtaking scope of the Clone Wars.