For a long time, cutting taxes for the poor was a major emphasis of the Republican Party. One reason that many poor people no longer pay federal income taxes is that they qualify for credits such as the earned-income tax credit, which has its roots in conservative thinking and has long been supported by members of both parties as a way to help the poor without increasing welfare payments or raising the minimum wage. The credit was added to the tax code when Gerald Ford was president, and was expanded by Republicans and Democrats, including President Ronald Reagan, who called it “one of the best anti-poverty programs this country has ever seen” in 1986.

President George W. Bush, for his part, doubled the child tax credit, and his tax cuts erased the federal income tax liability for millions of households.

And even as he attacked the entitlements of nontaxpaying households, Mr. Romney has pledged not to raise the share of taxes paid by families making less than $200,000 a year — a promise some analysts say is difficult to square with his proposal to cut tax rates and eliminate tax deductions. And he has proposed eliminating the taxes they pay on interest, dividends and capital gains.

Donald B. Marron Jr., the director of the nonpartisan Tax Policy Center, whose analysis Mr. Romney cited on the tape, said the tax code, by design, often aids the working poor. “This is due to longstanding, structural decisions in our tax code,” he said.

In any case, the debate within the Republican Party promises to continue. On Tuesday, many conservatives criticized Mr. Romney’s comments, and some Republican candidates for the Senate distanced themselves from them. Many others said that they supported his underlying ideas.

“There’s something mistaken about his analysis,” David Azerrad of the Heritage Foundation, a right-of-center Washington research group. “But there is something in the substance that points to something correct. There is a shift in our relationship with the government that we’ve witnessed in the past century, with more people ensnared in the tentacles of the welfare state.”

But both political parties have contributed to the growth of entitlement spending, and the benefits have not accrued just to Democratic voters as Mr. Romney suggested on the video.