Meaning some employers would rather not pay market-clearing wages. Funny how the free market suddenly ceases to operate when the wide open border is threatened.
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.