Given that there is high demand for web developers right now and software engineers in general?
Not in the near future.
why do you say that? it seems like everyone and their mother are trying to get into software development
I don’t think we are in danger of having a saturated market any time soon.
I have found though that there is an imbalance in the number of Junior Developers compared to the number of advertised roles that would accept a Junior Developer, at least locally here in Australia (although I suspect it’s an issue elsewhere, too).
I think many companies may have to adjust their expectations about the degree of experience they should consider in their software roles - because I see lots of roles suitable to mid, senior, and principal developers. There are more roles available than there are developers that meet those criteria, while there are many Juniors eager to break in to the industry.
Juniors need to do a better job also of communicating their worth to these employers, and doing the hard work to get their foot in the door.
But to return to your original question, no - I still think there are jobs for everyone, providing arbitrary obstacles aren’t put in place.
You also have to take into account that the need for web development is still growing. More and more stuff is happening online and someone is going to have to build all those apps, sites, and other web property.