1. In an insurance scheme you don't pay in expecting to get the same amount back. You risk pool with lots of other people. It makes no sense to get upset that other people make a claim on the same insurance scheme that you pay into - if you said "I haven't had a car accident I shouldn't have to pay for the people who do" then that would be silly.
2. Why do you pool risk? You know statistically, some people have car accidents/get robbed/get cancer (depending on what the insurance is). But you don't know who. So you make a small payment for the guarantee that if you are the unlucky one, you are covered by everyone else's small payments.
3. Levels of payment in a private insurance system are often determined by the degree of risk you present - if you are more likely to get sick/robbed/injured then you pay more. Some laws exist to restrict some discriminatory practices - for example, men have more car accidents, women live longer, so they're more likely to make a claim on the money pool, but some places have laws prohibiting different premiums on gender grounds in car or health insurance.
4. Public goods like a welfare system or a health system are an insurance scheme, they operate on the same principles as private insurance. Unemployment benefits are unemployment insurance. Old-age pensions are "living too long and running out of savings" insurance. Disability payments are "getting disabled" insurance. And a public healthcare system is health insurance. (Actually, nearly everying government does is a form of insurance - even defence, law and order, etc, are social goods we fund collectively. We pay in, not expecting to get a direct financial return equivalent to what we pay in)
4.a. (private v public debates are actually just a debate about which insurance goods are important enough to be universally and mandatorily supported by taxes instead of optionally available through private arrangements. The extent of such public arrangements is, crudely, determined on a case-by-case basis by the political process. eg: we all agree on defence and law and order, most of us agree on public education and public health insurance and government-guaranteed bank deposits, fewer agree on social housing, etc)
5. Just like a private insurance operator, these mandatory public insurance schemes pool risk. Everyone pays in, via taxes. The mandatoryness is usually necessary for them to be effective, particularly with pensions, unemployment benefits and health insurance. Because these things are insurance, you do not get the same value back in payouts that you put in. This is because the benefit from membership isn't the payout, but the guarantee that a payout exists, should you need it. The benefit from membership is reduced exposure to risk through risk-pooling.
6. Therefore, abolishing these things is depriving everyone who paid taxes the continued benefit of ameleorated risks, depriving them of the benefit itself. They no longer get the benefit of those risks being covered.
7. The Tea Partiers have therefore been benefiting from these arrangements all their life, just like you benefit from having car insurance even if you never make a claim. Even when they had a job, the guarantee of the availability of social security payouts was there. The fact that they got the payout doesn't change the situation at all.