There's no impact on wages for low-skilled workers with increasing supply of said workers as the market is already flooded with low skilled workers. It's not like you can pay them nothing. It doesn't make sense to bring in millions of unskilled workers when many of those jobs will be eliminated with automation, whether it be fast food kiosks or robots that can be machine-learned to pick fruit (futuristic for sure, but prototypes already marketed). At that point all that you have is yet another class of people who have no futures other than government handouts or resorting to crime within their own unassimilated communities, which will hopefully be lessened once the drug war is ended. But I'm sorry, just like the US shouldn't be Team America world police, it also shouldn't be a welfare haven either.
I think it's pretty far from a welfare haven, especially if you compare it to Europe.
That being said, I'm not a fan of bringing in hordes of low skilled immigrant workers. You can't pay them nothing, but they are often being paid well below market price. That puts a strain on your domestic workers who are forced to agree with lower wages and it results in dire living circumstances for the immigrant workers. It's a lose lose. To make matters even worse most of the time immigrants are those who are willing and able to take risks, e.g. young people., which in turn means that the country they are leaving is drained from valuable human potential.
As stupid as it may sound, I think so much in this world is squandered through greed.
We should strive to improve things all around the globe, which will in turn improve our own society. It's inexplicable that in a time where we have dozens of ways to communicate live with people from all around the world we still have mass immigration.