I suspect the current unemployment payout system allows people to afford to be picky and also drives wages upwards but artificially so. It allows for labor demand to increase during opening while holding the labor supply back. An open border will run counter to all this.
Some Americans might wait too long and might lose out on finding any work (once jobs get filled). Eventually, all systems will balance out, wages & pricing/value but at higher prices (inflation). Plus, there might even be devaluation of our dollar(s) if they increase currency in circulation. Taxes of all sorts will likely be increased as well so that it hurts less in any given pocket but overall it won’t be pleasant for anyone except maybe the new illegals.