According to Forbes (courtesy of the Tax Prof Blog), Newt Gingrich's tax return shows that he purported to avoid $50,000 of Medicare payroll taxes by using the so-called John Edwards Sub S tax shelter - a scam that Forbes says the IRS has "consistently and successfully attacked." The trick is to avoid the 2.9 percent Medicare payroll tax by forming a shell entity that supposedly employs you. Then, when others pay for your services, the money goes to the entity, which underpays you from a reasonable compensation standpoint. This ostensibly results in converting the lion's share of your compensation income into business profits, which do not face the Medicare payroll tax. If you actually need the cash, you can still ask the entity to pay it to you (and it will probably say yes to its 100% owner), but you label the payments as dividends, which also are exempt from the Medicare payroll tax (and indeed are tax-irrelevant, given that a subchapter S corporation is taxed as a flow-through entity whose profits accrued to you anyway).
Essentially, the trick is the same as if I were to make a deal with NYU whereby I formed a subchapter S corporation, charged NYU my entire salary, and then had my S corporation pay me just a pittance under the salary label. If this worked, I could avoid all payroll taxes (except on the pittance that I admitted was salary) - Social Security as well as Medicare. And I suppose NYU could avoid paying its half of the Social Security payroll tax. But needless to say this wouldn't actually work, in particular given the personal service corporation rules (Internal Revenue Code section 269A).
The John Edwards Sub S tax shelter typically comes closer to being legally defensible, avoiding the terms of section 269A and being contested by the IRS on "reasonable compensation" grounds, which in this setting is a version of substance over form. That is, if Gingrich the sub S owner were dealing at arm's length with Gingrich the star employee, he would have to pay himself pretty much the entire profits, since he is the asset. The IRS has had prominent recent wins lately in litigating this issue.
It's only fair to compare Gingrich's Sub S tax shelter to Romney's use of Caymans entities to avoid unrelated business income tax (UBIT) with respect to his pension investments. Romney's strategy appears clearly to work as a legal matter, and the tax he is avoiding (the imposition of UBIT on debt-financed exempt entity investments) has contested merits, which may be one reason why Congress has not revised the rules to defeat the strategy (an almost absurdly simple one, based on not "looking through" a meaningless blocker entity). Gingrich's tax planning trick strikes at the heart of taxing earned income under the rules that are supposed to apply to it. Like so many abusive tax shelters, it appears to be based on mischaracterizing actual transactions, rather than merely exploiting a legally relevant technical lacuna in the law. What is more, if audited, Gingrich (unlike Romney) might face a risk not just of losing the case, but of owing penalties.