In other words, they contribute labor to the economy, but largely freeload when it comes to any government-provided benefits.
Under the table work is not because they don't want to pay taxes, they'd be happy to. It is because they get paid by employers that prefer to hire cheap immigrants rather than to pay wage taxes and other withholdings.
One mans freeloading is anothers profiteering.
They are also quite limited in what government provided benefits they can partake in. Mostly the stuff that is already there for everybody else (infrastructure) as soon as they need more than that they are usually discovered and deported. Cheap labour is only good as long as it is cheap.
What government-provided benefits? Surely our largest two entitlements are social security and medicare, right? Illegal immigrants don't qualify for either of those. Importantly, many businesses use fake SSN's when hiring illegals, so often times they actually are paying FICA taxes -- with 0 hope to collect.
Public schools? Schools are largely funded via property taxes and sales taxes, both of which illegal immigrants pay at rates probably greater than the average American pays.
Income tax? They are some of the lowest paid people in the country, if they were suddenly legal, they'd likely be owed income taxes via the EITC or other mechanisms.
Emergency Care? Indigent care is expensive, but some state-level medicare programs are allowing illegal immigrants to actually pay for their care.
The entire 'freeload' argument is easily dismantled if you consider the actual facts for more than a few seconds.
Taxes pay for civil infrastructure, a somewhat-functioning democratic government, our National Parks, and of course our armed forces. We don't often think about these things since they're not as visible but our ability to sit here in the relative safety of our homes/workplaces exercising our 1st Amendment rights is in a large part supported by the taxes we pay.
http://www.itepnet.org/wp2009/tx_whopays_factsheet.pdf
Illegal immigrants are surely in the lowest 20% bucket. What taxes don't they pay? They rent homes, so they pay property taxes. Their money is spent on clothes and food, so they pay sales taxes. The income taxes that they might not pay are an absolutely minuscule portion of their burden -- literally $11/year on average.
Ever since the I-9's existence, most employers use fake social security numbers for their illegal immigrants. So FICA taxes are removed from their paychecks -- and they'll never get them back in the form of Medicare or Social Security. (Don't take my word for it, here's NYT reporting on SSA's "Earnings Suspense File": http://www.nytimes.com/2005/04/05/business/05immigration.htm...)
Smarter people than myself have looked at this, here's a good example: http://www.itep.org/pdf/undocumentedtaxes.pdf -- Tl;Dr: Illegal immigrants pay a lot of taxes, probably pretty close to the amount they would pay if they were legalized. However, they get far less benefit from their taxes since they don't qualify for most programs.
Second, they are not eligible for benefits, of any kind. Children who are born here to immigrants are eligible for benefits, because the children are American citizens, and also children who are brought into the country as children are allowed to attend school etc., because being children they were below the age of legal responsibility at time of entry.
Third, a lot of immigrants do pay taxes. Some use someone else's social security #, in which taxes are withheld but don't benefit them, some people work with an Individual Taxpayer Identification Number, which is like an SSN but not the same and which the IRS gives to people who are liable for US taxes but not eligible for an SSN. The usual way people file with an ITIn is as self-=employed, in which case they pay both the employer and employee portion of payroll taxes (which normally go into social security) but accrue no benefits for doing so.
Some people get tax benefits through the Earned Income Tax Credit which is a payment to people who work but have a low income, I think this amounts to something like $4 billion a year, against about $10bn paid in. It may be they're eligible for the EITC because a tax credit is not considered a benefit for legal purposes but I've never looked into that so I might be wrong.
That's not true at all. When California tried to cut off state benefits for illegals a federal judge force the state to reinstate them. Illegals send their (illegal) kids to school, even college, at taxpayer expense. They take advantage of community medical services, live in subsidized housing, and get assigned public defenders. That's just what they're entitled to under the law.
But if they have enough forged documentation to get a job they have enough to get food stamps and WIC too. Some of them do, though for political reasons the government isn't trying to figure out how many or how they could be stopped.
However, it's still important to acknowledge the fact that a small number of immigrants get sick, or descend into alcoholism, or get hurt badly enough that they can't really work. It's just the kind of thing that can happen to anyone.
I've grow up around a lot of immigrants, illegal and legal, and they have pretty much all been decent, hard-working people, and they have the same kinds of financial/family/emotional problems that everyone else has.