"Obama is not well known in the African-American community. He's still finding his voice and his presidential rhythm," she said. "But the more Obama talks about his vision for the future — and if African-Americans see themselves playing a role in that — the more African-American voters he could attract."
Public opinion polls suggest the black community has been fairly split over Clinton and Obama.
Clinton had an early lead over Obama among likely Democratic black voters, with 60 percent saying they supported her and 20 percent saying they supported Obama in an ABC News/Washington Post poll released February.
However, recent polls suggest Obama has made significant inroads among black voters.
Obama has 46 percent support among leaned Democrats to Clinton's 40 percent, according to the latest ABC News/Washington Post poll released at the end of July.
Brazile said former North Carolina Sen. John Edwards, who is polling at 6 percent among likely Democratic black voters, according to the latest ABC poll, hasn't given up wooing them.
Axelrod told National Journal that Edwards "should not be underestimated" especially in the early voting state of Iowa.
"Senator [John] Edwards has been camped out there for five years. And he's got a lot of good relationships there and a lot of strength."
In a newly released ABC News/Washington Post poll, Obama is tied with Clinton and Edwards for support among likely Iowa Democratic caucus goers, bringing in 27 percent, 26 percent and 26 percent of the vote respectively.
Democratic strategists say the emphasis on which candidate will win over blacks is recognizing an important voting bloc.
"These candidates know they can't take the African-American vote for granted," said Brazile. "The can't just just drive by the black communities and only come in at the end like they used to."
"There has been a vigorous courting of the African-American community, which is a good thing," said Democratic strategist Paul Brathwaite. "They are going state by state and city by city speaking to issues of importance to African-Americans."
But, he said, black voters, like others, haven't made up their minds yet on whom they will support.
"It's not a done deal by any stretch of the imagination."