"The Boeing 737 is the best selling commercial aircraft in aviation history with almost 10,000 aircraft ordered." 

So crows The Boeing 737 Technical Site, a U.K.-based website for 737 enthusiasts. But in fact, the site probably understates the case. Earlier this month, Boeing (BA 1.51%) announced the delivery of its 7,370th 737, which flew off to new customer Lion Air of Indonesia on Nov. 5. Add to these 7,370 planes already delivered another 2,845 as-yet-undelivered 737s sitting in Boeing's backlog, and the 737 tops 10,000 units ordered quite handily.

So... "best selling" indeed. But that does pose a problem for Boeing.

A plethora of riches
Boeing's most recent 10-Q filing with the SEC lays out the problem clearly. Boeing owes its customers 2,845 planes. It's currently producing the birds, however, at the rate of only 35 per month. That's up from 31.5 planes per month earlier this year, but even so, it means that Boeing's backlog on the 737 alone now runs to six years, nine months -- and that's if it sells not a single new 737. (In fact, though, sales of the new "MAX" variant are already through the roof, recently topping 900 units of this model alone.)

On the one hand, that's a nice problem to have. There's not a lot of businesses out there that can guarantee you a rock solid revenue stream nearly seven years long. On the other hand, though, look at this from the perspective of the customer. Say you need a new plane now. Say you want to place an order with Boeing. How are you going to react to being told "get in line, we'll have it ready for you in... 2018"?

Think you might give Airbus a call and see if they can turn around your order any faster than that? Think you might even give an upstart like Canada's Bombardier a chance to win your business, if they offer a sweet enough deal on a shiny new CSeries?

You can actually see this happening, in fact, over in China, where Boeing's backlog on the popular 737 is likely contributing to the success of local plane builder Commercial Aircraft Corp (COMAC), which just landed 50 new orders for its C919 regional jetliner. This week, domestic operators Hebei Aviation and Joy Air each signed up for 20 new C919s. Meanwhile, General Electric's (GE 1.30%) GE Capital Aviation Services has doubled its initial order of 10 C919s. Boasting engines and avionics from recognized Western airplane parts suppliers like GE and Rockwell Collins (COL), COMAC is even starting to attract interest from international buyers, including a sister airline of British Airways.

Time to motor?
So what's Boeing to do if it wants to keep its current customers happy, and not discourage potential new buyers? Simple: It must build planes faster. Already, the company has announced plans to ramp production up to 38 planes per month by early next year, followed by a jump to 42 planes per month in Q2 2014. The Boeing 737 Technical Site thinks they'll go even further, recently asserting that Boeing has a plan to open a new assembly line and increase production to 60 aircraft per month. That's nearly twice today's pace -- two entire passenger planes, fully outfitted, rolling off the assembly line every day.

Incredible as that sounds, Boeing seemed to confirm the theory in a statement yesterday, noting that a new production line under construction in Renton, Wash., that will be building the 737 MAX will "eventually" be used "for future rate increases." According to the company: "We don't have any specific plans when that next rate increase will be, but we're pretty sure it's coming."

Danger: turbulence ahead
For the record, investors seem to see a big opportunity coming, too. Wall Street analysts expect to see double-digit profit growth at Boeing over the next five years. But the Foolish question to ask here is: What if it doesn't come? What if the beaucoup growth of the global air travel industry gets delayed? After all, it's not as if it's all that hard to cancel even a supposedly "firm" order in the airline business. Why, just a few months ago, Quantas wiggled out of an order for 35 Boeing Dreamliners, citing little more than a "change" in its "circumstances."

And it's not only Qantas finding its need for new planes may be less urgent than it once thought. Last quarter, revenue at Delta Air Lines (DAL 4.05%) grew a bare 1% in comparison to the previous year. Sure, China's doing better than that. But rumbles of an economic slowdown can be heard even over there. If you take Chinese travel agency Ctrip.com (TCOM -0.36%) as a rough proxy for the industry, for example, well, revenues were up 20% at Ctrip last quarter.

That's a good number. Don't get me wrong. But does even a 20% growth in business in China justify predictions that Boeing will need to nearly double the rate at which it builds its planes to keep up with demand? Seems to me, the danger here is that Boeing cold be overbuilding to satisfy demand -- demand which may evaporate in the absence of a strong economic rebound.