The popular belief that illegal immigrants do not pay taxes is simply not true. As a Chicago immigration attorney, I have seen a growing trend from the government immigration office to deny any pending immigration application if the applicant has failed to pay taxes. This is true regardless of whether the applicant's income was through legal or illegal work authorization.
Essentially, the immigration laws prohibit an alien from obtaining a green card if they have committed a crime of fraud. Tax evasion has increasingly been interpreted as a type of fraud which negatively affects an immigrant petition.
Filing returns does not require a social security number. An alien may apply for a Tax Identification Number (TIN) with the Internal Revenue Service (IRS) to pay their taxes and have a written record of their filings. These receipts will be useful when the time comes to adjust status and apply for a green card.
There are many reports recording the "trend" of illegal immigrants paying taxes like it is surprising, but when you weigh the consequences of not filing a tax reutn against their future potential green card, it becomes plainly obvious that illegal immigrants have every incentive to pay their share of taxes. Reports often cite that illegal aliens will not pay taxes because they do not share in other government benefits, like social security. But that reasoning is short-sighted and often times, immigrant families plan their transition to the US in terms of long-term goals.