They are going to be paying payroll tax. At the end of the year, any witholds as to income tax are going to be given back, and I believe they would qualify for Earned Income Credit and other credits. Social Security they may pay, but in the end, they won’t be paying income tax.
I have always thought that the quickest way to reduce illegal immigration is just to set the tax rates higher for non-citizen workers. So the payroll tax, for example, could be 20% instead of 12.4%. And to keep the liberals happy the burden could be on the employer. Also no EIC for non-citizens.
What employer would take the risk of hiring an illegal immigrant if it meant the IRS could show up a couple of years later and recover the taxes you failed to pay - plus penalties, interest, etc.? Nobody, since we all know the government would be out looking for any illegal immigrant they could find on a business' payroll since they would be a goldmine of taxes and penalties.
Also, any illegal immigrant who didn't pay the tax would be a tax evader, and there is no way the federal government is going to look the other way at that. They need the money too much.
Illegal immigrants already pay tens of thousands of dollars to smugglers. Why not capture that money too - charge fees for expedited visas.