Mr. Romney also said at the debate, “I don’t have any plan to cut education funding and grants that go to people going to college,” but his education plan says he would “refocus Pell Grant dollars on the students that need them most and place the program on a responsible long-term path,” suggesting that fewer people would qualify.

The Romney campaign rejected the notion that Mr. Romney had shifted to the middle in tone or substance to woo independents, noting that he said little in the debate that he had not said before. In describing Massachusetts’ health care law as “a model for the nation, state by state,” aides noted, he was reaffirming his position that states, and not the federal government, should make such decisions individually. And they noted that Mr. Romney’s debate performance was praised by many conservatives — Rush Limbaugh, Erick Erickson of RedState.com, William Kristol of The Weekly Standard — who have been critical of him in the past.

Kevin Madden, a spokesman for the Romney campaign, said that Mr. Romney had spoken about his past bipartisanship to indicate his ability to get things done. “This idea of bipartisanship, sitting down with people across the aisle and working on all these issues together, that’s something that appeals not only to people in the middle who are undecided, but to people on either side who look at a Washington that is not getting anything done,” Mr. Madden said.

But Mr. Romney’s change in tone on taxes was especially striking. He wants to cut income tax rates across the board by 20 percent and make up for the lost revenue by eliminating or reducing tax breaks — without raising the share of taxes paid by the middle class. A number of economists and independent analysts have said that it is not possible to achieve all of those goals, because cutting everyone’s taxes would result in the loss of so much revenue that it could not be made it up without raising taxes on middle-income Americans by ending some of their tax breaks, too.

While Mr. Romney has always said that his proposal was designed to be revenue neutral, because the cut in tax rates would be offset by the reduction in tax breaks, he sometimes described his plan as a tax “cut” when facing conservative opponents during the Republican primaries.