If supply expands to meet a rise in demand, supply is elastic. If demand contracts to meet a fall in supply it is elastic.
If, in either case, supply or demand doesn't change, it is called inelastic. The domestic labor supply is an example of inelasticity. It doesn't expand to meet a rise in demand(higher wages). For several reasons.
First, it takes many years to produce a new worker.
Second, the birth rate has been depressed for 30-40 years.
Third, the labor supply is aging, so there are fewer and fewer workers to do the hard and dirty work.
Fourth, the labor supply is better educated and they don't have to do the hard and dirty. Additionally there are fewer and fewer educational drop-outs to do the hard and dirty .
So in this situation, a rising demand for domestic labor(higher wages) will not create and expanded supply.
Nice try, but elasticity isn't the issue, since the last time anyone looked in America there aren't assigned jobs and the labor force is free to move to where the money is.
Now, let me explain it in simpler terms so that you will have better understanding: Turn your page to "market clearing wages". Bid up wages and surprise, surprise, you get more people willing to do the work.
But then, those who have been making money by using illegals don't want to pay market wages. They prefer to insist that they deserve to have their labor force subsidized by the taxpaying public. Somehow they shouldn't be subject to the economic forces everyone else is, such as going out of business if they aren't competitive.