There are two popular models to predict long term employment trends.
Model 1) There's a finite amount of work out there. Computers will replace mental jobs just like robots killed physical jobs. We're all heading towards unemployment.
Model 2) Employment is determined by the value of an employee. Technology makes employees more valuable, not less. Employees will get more bargaining power as technology improves, not less.
The economic consensus is with #2, because feedback systems appear to drive down high unemployment over time (though bad governance can definitely interfere). One feedback system might be: idle people will eventually conspire to discover and meet the wants of others.
That's abstract though, it might be helpful to look closer to home.
Consider the fear that software will take over everyone's work. It's easy to forget that programmers know exactly how this goes. They have already cannibalized a lot of their work with software. The last fifty years of programming language (IDE, engine, ...) development has been a steady progress of finding ways to get software to write software, to do all the annoying grunt work of the job.
As programmers became more efficient, and crank out more and more complex tools over time, has the demand for code steadily decreased? Have we now solved all the world's problems that can be solved through code? Or has the problem space expanded to meet our capacity? Has the demand for programmers increased because their time is now much more valuable than it was in the era of punch cards?
Note more broadly, jobs are picking up right now as part of the recovery, despite continual technological improvement.
I think the economic consensus is with #2 because so much of the available data so consistently points that way, so it's easy to dismiss the other model as just natural human pessimism about the future. Maybe the pessimistic model is right and we just don't know it yet, but I think it currently has the weaker case.