They'd be problems generated by mishandling of tax money yet again. The population generate the tax and the government spend it where they think necessary. If hospitals and schools are overcrowded it's a result of poor planning and administration not due to over population. Or are you going to try to tell me that the tax receipts aren't big enough to fund the nhs and education system?
Go back to my earlier post regarding a city the size of Leicester needing to be created every year to cope with the net migration. They need 150k houses, 3 hospitals, 100 schools, etc. and I don't think that the immigrants will generate the money needed to fund that (and the people to work in them) in their lifetime. There is only so far that you can extend existing services.