Large employers (or any other corporations) don't see labour costs as an end in it of itself, but merely means to an end: the ends being (whether in the long term or in the short term) making money. They could pursue the ultimate "throw more bodies at the problem" strategy, but per Brooks it is known not to work; companies that do so are penalized by the market.
On the other hand engineers can't choose between working many low-satisfaction jobs simultaneous or working for one high-satisfaction job -- so they choose jobs that maximize their satisfaction. While there's low marginal value in higher salaries past a certain point (so other factors, e.g., for me it's working on interesting things take over); however, significant sub-market compensation (in terms of both salary and stock) -- compared to what an individual of similar ability, experience, and location would get in a company of similar size, age, etc... -- does greatly decrease satisfaction.
That gives: engineers want to maximize their satisfaction which requires not being underpaid; companies want to maximize the money they make, but can take many different approaches to this.
So at the end, the market "chooses" to hire fewer, but strong engineers through a combination of university recruiting (and paying high salaries even to new graduates), tolerating a certain degree of churn among early-career software engineers, and also aggressively going after a smaller cadre of experienced programmers who can also mentor talented but less experienced new-hires and interns.
So no, I don't see the scenario you describe as happening. Instead, I'm not alone (http://en.wikipedia.org/wiki/Average_is_Over) in thinking that similar trends will occur (or, rather, are already occurring unseen) in other white collar jobs, as well as many skilled blue collar jobs. Company finance departments will want to hire workers who are able to write VBA and not rely on clunk recorded macros; manufacturers will (and already do) want to hire workers who can program a CNC machine[1]. This will not make them software engineer any more than me being able to solve a differential equation makes me a mathematician or understanding logic circuits makes me an electrical engineer (to take it one layer lower, knowing Maxwell's field equation and even using it on the job, doesn't make an electrical engineer a physicist). Circling back, this is exactly why it makes sense for people to learning programming -- if robots are automating large parts of people's job's, there will jobs that require knowledge of both the job and programming, to be able to write "userland" programs on the robot, as oppose to program the robots' embedded systems (or to write Excel VBA scripts as opposed to build Excel itself, etc...)
[1] Language they use is G-code (http://en.wikipedia.org/wiki/G-code -- note the date, it's nothing new), and yes, it's Turing-complete: http://callenblogi.blogspot.com/2011/03/bf-interpreter-in-g-...)