Illegal Immigrants help?

Of course the illegal immigrants do not get all the goodies such as education and health care, and yet they pay their fair share of taxes in sales, property, municipal, payroll and even federal income tax. I have just learned that those unable to find jobs in their own countries just cross the border and come to the US, because work is plentiful and illegal wages are substantially higher than at home. I have heard that America won't run without all those illegal immigrants working in every part of the country. If they weren't illegal, they wouldn't be doing all the dirty jobs that Americans don't want to bother doing.