"I know the president has said he will do those things. But he has not. He cannot. He will not," Romney said as the crowd's murmurs turned to groans.
At other points, Romney earned scattered clapping for his promises to create jobs and improve education. In an interview with Fox News after the speech, Romney said he had expected the negative reaction to some of his comments. "I am going to give the same message to the NAACP that I give across the country, which is that Obamacare is killing jobs," he said.
Four months before the election, Romney's appearance at the NAACP convention was a direct appeal for support from across the political spectrum. As for Romney's contention that his policies would help "families of any color" more than Obama's would, White House spokesman Jay Carney said the president had pursued ideas that help support and expand the middle class after a devastating recession, and that as part of that, black Americans and other minorities had benefited.
Obama spoke to the NAACP during the 2008 campaign, as did his Republican opponent that year, Sen. John McCain. The president has dispatched Vice President Biden to address the group Thursday. Obama is scheduled to address the National Urban League this month.
Within minutes of taking the stage, Romney made note of his opponent's historic election achievement - and then accused him of not doing enough to help African American families on everything from family policy to education to health care.
"If you understood who I truly am in my heart, and if it were possible to fully communicate what I believe is in the real, enduring best interest of African American families, you would vote for me for president," Romney said to murmuring from the crowd.
Romney added: "I want you to know that if I did not believe that my policies and my leadership would help families of color - and families of any color - more than the policies and leadership of President Obama, I would not be running for president."
Romney's criticism of Obama didn't set well with some in the audience.
William Braxton, 59, a retiree from Maryland, said: "That really took me by surprise, his attacking Obama that way."
Left unsaid by Romney: any comments on a series of new voter-ID laws that critics say are aimed at making it harder for blacks and Hispanics to vote. At the convention a day earlier, Attorney General Eric H. Holder Jr. labeled those laws "poll taxes" - a reference to the fees used in some Southern states after the abolition of slavery to disenfranchise black people.
Romney expressed support for voter-ID laws during a late-April visit to Pennsylvania, which now has one of the toughest statutes in the nation. "We ought to have voter identification so we know who's voting and we have a record of that," Romney said then.