NEW YORK (CNN) -- Barack Obama made history Tuesday night when he became the first African-American in U.S. history to clinch a major party's presidential nomination. But the Illinois senator faces several challenges as the campaign now turns to the general election -- notwithstanding a first order of business of helping to heal the wounds of a deeply divided Democratic Party.
Obama offered an olive branch to rival Hillary Clinton on Tuesday evening, telling supporters at his victory rally in St. Paul, Minnesota, that the country and the party "are better off because of her." He added that Clinton has "an unyielding desire to improve the lives of ordinary Americans, no matter how difficult the fight may be."
Obama and Clinton rounded out the 2008 Democratic primary season by splitting the final two states: Montana and South Dakota. And despite his loss in South Dakota, Obama gained enough delegates to cross the finish line an hour before the Montana polls closed.
As the campaign shifts to the general election, Obama would certainly prefer to commit all of his energy to presumptive Republican nominee John McCain. But the final exit polls, however, indicate he still has work to do to unify his fellow Democrats.
In both South Dakota and Montana, roughly one-third of Clinton's supporters said they would either vote for McCain or stay home in November. Over half of Clinton's voters said they would not be satisfied with an Obama nomination. Her voters were evenly split on the question of whether Obama is honest and trustworthy.
The presumptive Democratic nominee is also still struggling to win over the support of Democrats at the lower end of the socioeconomic ladder. Specifically, white Democrats without college degrees have not yet fully embraced his candidacy. In South Dakota, non-college educated white voters backed Clinton by 22 points (61 to 39 percent). In Montana, Obama's performance was better, as he edged out Clinton by five points (48 to 43 percent).
If, however, Obama does not to find a way to significantly strengthen his support with this critical Democratic constituency, he will likely need to compensate by dominating the independent vote or attracting large swaths of traditionally Republican voters in November.
To do so, Obama is likely to need the strong support of Clinton in the months ahead. The question of how these two bitter rivals come together to help unify the party has not yet been answered. Some of Clinton's supporters are calling on Obama to tap her as his running mate, but it's unclear whether these two rivals can overcome the deep divisions of a divisive primary season. Watch the twists and turns of the Democratic primary season »
Clinton, in her speech to supporters Tuesday night in New York, said she was "committed to uniting our party so we move forward stronger and more ready than ever to take back the White House this November."
But the one-time Democratic front-runner neither conceded the nomination nor offered specifics about what steps she would take to follow through on her declaration.
"In the coming days, I'll be consulting with supporters and party leaders to determine how to move forward with the best interests of our party and our country guiding my way," she said.
Two of Clinton's top supporters, though, signaled they are ready to close ranks and help Obama take back the White House, which has been under Republican control ever since her husband, Bill Clinton, left office in January 2001.
James Carville said he is ready to open up his wallet to help Obama build a political war chest to take on John McCain in November.
"As soon as she gets out I am going to write him a check," said Carville, who is a CNN contributor.
Clinton campaign chairman Terry McAuliffe said late Tuesday afternoon -- prior to CNN projecting that Obama clinched the nomination -- that he too would help out the Illinois senator.
"If he is the nominee, listen, I will help," McAuliffe said. "I have helped Democrats now for 30 years, and I will continue to do so."
While Carville and McAuliffe agreed that the two Democratic rivals would join together to help unify the party, Carville noted that there needs to be time for a healing process as the party prepares for the general election.
"I think the easiest Democrat to win over is Sen. Clinton," Carville said. "She will be as helpful as she can be."
But Carville also said that the burden to bring the party together needs to be a joint effort, noting that feelings from this competitive primary are "still kind of raw."
"She is going to do her part, and he is going to have to do his part too," Carville said.
McAuliffe predicted that Clinton and Obama "are going to work very close together," adding that "They both need each other."