That's what you need. Forty paid quarters to recieve social security. It's ten years of full-time work - most people easily accomplish this before becoming eligible to recieve social security benefits.
I worked in the elder unit of a legal services organization after my first year of law school. Forty quarters was the first thing I learned, after when to take lunch and where to find the library.
None of our clients were under sixty, so most were eligible for social security benefits, by age. Unfortunately, many, many, were not eligible because they did not have enough paid quarters. People who immigrated late in life were vulnerable; more so if they'd ever been self-employed, worked as day labor, or providing household services. Especially women - even women who had never been married, and never had children. These women were particularly bad off, because they were less likely to have family support, and couldn't recieve benefits based on a spouses' work history.
If your boss doesn't pay social security taxes - you don't get a paid quarter. So every quarter of sitting, housecleaning, nannying, paid-companioning, personal care assitanting, under-the-table anything - doesn't count - unless your employer took the trouble to pay your taxes. Which they usually don't.
Worse,employers often present this as a good thing for the employee - "Hey! I can pay you more - we don't have to report any of this."
It may be too late for H.Lawstudent's elderly clients, but a current household worker who is paid off the books has an option to take control of her situation, IF--and it's a big IF--she knows enough to do so.
She can file a Form SS-8 to request a Determination of Worker Status for Purposes of Federal Employment Taxes and Income Tax Withholding as well as a Form 8919 attached to her Form 1040 to declare uncollected Social Security and Medicare tax on wages not reported by the employer. This will allow her to accrue credits toward eligibility for Social Security and Medicare. It should also eventually cause the IRS to investigate the employer. Obviously, a nanny who is still working for the employer may be afraid to do this, because of the likely repercussions to her job. However, a nanny who has left her job could certainly take this action when she files her tax return the following year. If more parents hiring nannies knew this was a possibility down the road, they might be more likely to comply with the nanny tax laws from the get-go.
It should also be noted that if parents engage a "babysitter" to care for their child in the babysitter's own home (rather than in the child's home), then the sitter is generally NOT their employee, but rather is actually self-employed for tax purposes. The parents would have no obligation to file any employer paperwork or pay any employment taxes on the sitter in such a case. The care provider should file a Schedule C or C-EZ as well as a Schedule SE to declare her self-employment income for income tax, Social Security and Medicare tax purposes. This will enable the care provider to accrue credits towards Social Security and Medicare eligibility in her later years.