The most prominent of a new crop of the groups is the Karl Rove-affiliated Crossroads GPS – which raised $43 million in the 2010 midterm elections and is expected to become an even bigger force this year after pledging to raise and spend $300 million with its sister super PAC, American Crossroads. Democrats are also expanding their use of the groups, led by pro-Obama Priorities USA, which raised $2 million last year.

Precisely because they offer anonymity, such groups may be attractive vehicles for companies that want to spend money electing a favored candidate or pushing an issue. In 2010, Target generated a national backlash after giving $100,000 to a Minnesota group that ran ads supporting a candidate who opposed gay marriage. Liberal activists seized on the donation after it was revealed in state filings. If Target – or any other public or private corporation – gave to Crossroads GPS or Priorities USA, the public would never know.

Companies may also be deducting from their taxes the undisclosed donations they give to these groups.

"There has always been this suspicion, but I can't prove it," says Frances Hill, a tax law professor at University of Miami who first floated the concept in a brief mention in the New York Times earlier this month. "It could be put into the advertising budgets, which for many companies are very large dollar amounts."

This is where the aggressive interpretation of the tax code would come into play.

Corporations are allowed wide latitude in deducting business expenses from their taxes – everything from workers' salaries to marketing expenses of all kinds. But one thing they're explicitly barred from deducting is political expenditures.

As the law puts it, companies are not allowed to deduct money spent on "intervention in any political campaign" or "any attempt to influence the general public, or segments thereof, with respect to elections, legislative matters, or referendums."

But tax experts say a company could argue that money given to "social welfare" groups isn't political spending at all and that the donations are instead "ordinary and necessary" business expenses.

The company might argue, for example, that ads run by a social welfare group would favorably influence opinion on a public policy issue that affects the company's business. Thus, say, an oil company would claim a business expense deduction on a donation to a social welfare group that was running ads criticizing President Obama's policies on domestic drilling.

The company would also have to argue the money isn't being used by the groups on political expenditures. So it comes down to where the IRS draws the line on what is a political expenditure, and whether ads run by such groups as Crossroads GPS or Priorities USA would cross the line.

Determining what is and is not a political expenditure is a matter of intense dispute. The IRS has historically looked at various factors in assessing nonprofit spending – things like whether an ad mentions a candidate for public office or whether it's aired close to an election. But wiggle room remains.