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Nearly all advertising by new class of funding groups is negative, records show, and has heavily favored Republicans, with $14.5 million spent opposing Mr. Obama and $3.5 million opposing presumed Republican presidential nominee Mitt Romney, plus about $500,000 on pro-Obama ads.

The question is when a nonprofit has crossed the line on advocacy and political activism.

“The statute says a social-welfare group must be engaged exclusively in social-welfare issues. Courts have since said a group shouldn’t lose its tax status so long as its otherwise impermissible activity is only ‘insubstantial.’ Then the IRS published a guidance saying candidate-specific activity is fine as long as it’s not its ‘primary purpose,’” said Paul S. Ryan, a lawyer at the Campaign Legal Center (CLC).

“There’s a big difference between insubstantial and primary activity,” he said.

After the CLC inquired, the IRS sent a letter last month saying it would “consider proposed changes” to its rules.

But that in turn provoked the warning letter from Mr. Hatch and fellow Republicans.

“These petitions have less to do with concerns about the sanctity of the tax code and more about setting the tone for the upcoming presidential election,” the senators wrote.

Mr. Ryan said any fines the IRS levied would come well after the election — perhaps after the social-welfare group in question had already dissolved — and would represent a relatively small amount of money.

But some tea party groups trying to form as similar nonprofits said they had received requests for more information from the IRS.

The conservative American Center for Law and Justice announced it was aiding 26 groups that received letters, but eight of the groups have since been granted tax-exempt status and seven others have had the request letters retracted, said spokesman Gene Kapp.

Several liberal nonprofits also have spent millions of dollars in recent months, including Planned Parenthood Action Fund, at $3.3 million, mostly opposing Mr. Romney, and the League of Conservation Voters, at $2.7 million, on a handful of congressional races.