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The electability question for Mrs. Clinton often focuses on her sex, while Mr. Obama’s race is also considered a factor.

“I don’t know if we’re ready for a black candidate yet,” said Bernadine Fick, a substitute teacher from Onawa.

But Mr. Obama says he would help Democrats be competitive in Southern states such as Mississippi, touting that he can “rebuild the political map.”

“We’re getting new people involved,” he told the AFL-CIO forum. “We’re expanding the electorate. I can put in to play some places that haven’t been put in play in a long time.”

Citing the high population of black voters in Mississippi, he said: “Imagine if Republicans have to go down to Mississippi and spend some money, because right now they can just ignore the South because we give it to them.”

Mr. Obama said it is a “mistake” for Democrats to employ an electoral strategy that includes ignoring the South, rural areas and “faith voters.” Instead, Democrats should “show up everywhere and organize everywhere,” he said.

Mr. Biden, of Delaware, struck a similar chord Wednesday.

“I can win Kentucky, Missouri, Arkansas, West Virginia. I can win red states,” he said. “I will win 45 percent or more of the vote in 15 of those red states. If you elect a Democratic president without that — you won’t be able to implement an agenda that we all want.”

Mr. Richardson says although he is not considered a “rock star” like Mrs. Clinton or Mr. Obama, “It should be about who can win. I’m electable.”

Democrats too often nominate “Northeastern” candidates who aren’t “broadly based” enough to win “the middle of the country,” he said.

“I’m pro gun, and you know that hurts me in other states,” he said at the labor forum. “I have the values of the West and the Southwest. I believe I’m a candidate you can proudly back.”