I think, politically in the US, this will do him no harm at all. I also think Mrs May knows what she's doing politically by aligning herself with him. Sadly, I think there are huge numbers of people in the UK who will be saying "we" should do the same.
Blair then Cameron caused all this IMO by creating an environment where it was racist to even discuss immigration. It is a big problem for many poor communities in US & UK. It should have been dealt with properly years ago, rather than nice MC people pretending the country could afford to keep taking so many people as long as they didn't live next door or fill their schools
I think the current US policy is abhorrent but I'm sure there are large numbers who think it makes sense, which of course is why we have the current leaders in both countries.