Low skilled immigrants are often paid less, which means they're pushing the wages down. That's one downside. Also some might consider it a downside that native born citizens are losing their jobs and in case of welfare the immigrants might be straining it more than what would otherwise be the case.
For companies there might not be a downside but for some workers there for sure are.
But sometimes locals will not take the jobs that immigrants take even for a better wage. The immigrants that take those jobs in a dire enough situation to not be able to choose.
So I'd say it's an issue with society not the immigrants themselves doing the job no one wants to do for wages no one wants to have
It's because immigrants don't qualify for welfare because you need a social security number for it. Which immigrants don't have. It's pure propaganda, ignorance and/or racism from them.
So pretty much they all need to work to make money.