Keep in mind too that some number of those under the present tax system are missing (from the standpoint of tax payments) from contributions to even payroll taxes. I think it's less of a cut and dried system than you seem to believe.
“... will also be “contributing” to the tax revenues through the FairTax but they will not be eligible for SS and MC.”
You seem to think that is a good thing. Why ? It just means they are defenseless since they cannot vote against higher FairTax rates. So we’ll have a huge number of legal families that know they can vote themselves increases in SS benefits and somebody else will have to pick up the tab for it. See my previous post for examples with numbers.
While I am all for getting the underground economy to pay taxes for the national defense, it does seem unfair to force them to pay SS/M taxes if they will never be able to get anything back. Besides, have you considered the other side ? Say the person in the underground economy is a waitress who doesn’t report all her $40K tip income today. Under the FairTax, she’d report higher tips than she actually got in order to boost her SS benefit. HR25 actually has a provision that attempts to prevent that and limits reporting tips to the SSA to a max of $5,000/yr — so now you penalize waitresses that really do have $40K in tips a year, and they don’t get full credit toward SS. At least under the current system, when the waitress fails to report all her tips she saves taxes today but it hurts her SS benefit down the road.