The US is going to get to a population of 333,333,333 people in short order. Is that not enough?
While importing cheap labour and working them hard is a road to prosperity - probably quite a good one for all involved - it is hard to see how there can be a pure labour shortage with that many people, that much wealth and that much history of advanced manufacturing.
There is probably an organisational problem here somewhere.
The absolute number of people tells you nothing about the state of the labor market. Every additional person demands services, which creates jobs to fufill the demand, and then the employees of that job use their income to pay for goods and services they like, and the economy grows... that's the entire basis of capitalism and economics in general. The economy isn't a zero-sum game.
For example, when Orlando had a sudden influx of people move there from PR after Hurricane Maria: "we find that employment in Orlando increased, especially in construction and retail, and find positive aggregate labor market effects for non-Hispanic and less-educated workers. While we find that earnings for these workers decreased slightly in construction, this was balanced by earnings growth in retail and hospitality. These results are consistent with small negative impacts on earnings in sectors exposed to a labor supply shock, offset by positive effects in sectors impacted by an associated positive consumer demand shock."
Instead what you have is a sudden negative supply shock, due to the pandemic, while simultaneously having a demand shock for goods because of stimulus. Of course prices for the labor demanders will increase.
While importing cheap labour and working them hard is a road to prosperity - probably quite a good one for all involved - it is hard to see how there can be a pure labour shortage with that many people, that much wealth and that much history of advanced manufacturing.
There is probably an organisational problem here somewhere.