Canaccord Genuity analyst Ken Herbert says there will be pressure there, too--but not the good kind. From his recent research note on the production increase:
Longer term, this announcement supports the preference for original equipment suppliers relative to the aftermarket. We believe that airlines are already slowing 737 maintenance spending as rates have increased, and the useful life of the aircraft model continues to get shorter. This announcement will accelerate this process, especially if Boeing is able to maintain the higher 737 rate for more than just a few years.
At the back end of the market, there's indication that the availability of newer (and in many cases larger) models is pushing the earliest 737NGs into retirement sooner than some would have predicted.
Part-outs of early-build 737NGs have been frequent, albeit with recent indicators suggesting a slowdown. Aviation Week's Commercial Fleets database shows that of the 38 NGs retired from revenue service so far, at least 11 have been parted out.
Perhaps more telling is the average age of those 38 NG retirees: 11.7 years. For what it's worth--and some would argue not much--Fleets data peg the average age of the first 38-odd 737 Classics parked at 17.6 years.