While it is true that illegal immigrants pay taxes, they also receive more in tax services than they pay in taxes. Therefore, they are a net drain on our society.
I will agree with Sigma that the rules and the process for those we admit legally needs to be simplified to cost both immigrants and taxpayers less money to administer it and to place the requirements within bounds of reason.
However, we need to realize the needs of our nation are very different than they were 80 years ago and more. Our economy and our geographic footprint are mature, there is not the expansion to accomodate the immigration rate there was at that time. Our immigration policies need to be formed in our national best interest. The current limits and standards need to be revisited to ensure they match our needs.
No matter how the laws end up, they need to be enforced not only to prevent people from entering the country illegally, but to intercept and deport people who are here illegally. We need to prosecute the employers who hire illegal immigrants and fine them to an extent where it is in their economic best interest to obey the laws, to override the temptation of cheaper illegal labor. These fines could be used to cover the costs of the enforcement.
All government services and documents need to be solely in English. It is the responsibility of the immigrant to learn the English language.