(CNN) -- The titanic struggle for the Democratic candidacy neared its end Tuesday with final voting expected to push Hillary Clinton aside and usher in Barack Obama as the first ever black U.S. presidential nomination for a major political party.

After months of primaries and caucuses, the Democratic party still does not have a nominee.

Clinton's campaign chairman Terry McAuliffe told CNN Clinton will not concede at a New York rally being held after voting closes Tuesday night in the last two primary states.

That was a reaction to an Associated Press story quoting two senior Clinton campaign officials as saying she will concede Tuesday night or early Wednesday that Obama has done enough to secure the Democratic nomination, while stopping short of formally suspending or ending her race.

But Clinton told New York lawmakers she is willing to be the vice presidential nominee on Obama's presidential ticket, those lawmakers told CNN. CNN first reported Monday that Clinton was signalling the Obama campaign of her interest.

CNN confirmed that another big name Democrat, former President Jimmy Carter will endorse Obama.

Democrats in South Dakota and Montana cast the final votes Tuesday in a long and bitter campaign that has cost the candidates dearly in dollars and left the party struggling to unite to challenge Republican John McCain and succeed George W. Bush at the White House.

Obama needs the support of about 40 more Democratic delegates to make the 2,118 needed to capture the nomination at the party's August convention but he is likely to depend on superdelegates -- party officials free to back any candidate -- to tip the balance.

The Illinois senator, who has sought to dispel fears of inexperience by campaigning on a message of change, has emerged as favorite in recent weeks despite a dogged campaign by Clinton who as former first lady claims to have more political experience.

Although campaigns for both parties said there had been no formal discussion, sources close to Clinton said she was poised to acknowledge her inevitable defeat by Tuesday signaling her willingness to accept an offer of becoming Obama's running mate if asked.

"In her speech tomorrow night she will convey the message that first and foremost she is committed to Democrats winning in November and will do whatever she's asked to do," a close friend of the New York senator said.

Her husband, former U.S. President Bill Clinton, also told voters in South Dakota on Monday that "this may be the last day I'm ever involved in a campaign of this kind." Watch how the race could end »

Obama insiders are said to be split over whether a joint ticket with Clinton will be a good idea, with some doubting she can deliver, despite claims the pairing would help "ram down the animosity" between supporters of the two that many fear could cost the Democrats the election.

Democratic Party insiders are also discussing how to patch up Clinton's relationship with the black community and how to bring African American Clinton supporters into the Obama fold, several top Clinton supporters said.

Feuding between the two camps reached fever pitch at the height of the campaign, after Clinton and Obama saw off main rival John Edwards then traded blows on sideline issues including Obama's links to a controversial preacher and Clinton's claims to have dodged bullets in Bosnia.

At least one superdelegate -- the highest-ranking African American in Congress Jim Clyburn -- announced his endorsement Obama on Tuesday, saying Obama had "energized" constituents.

But despite forecasts of defeat, Clinton -- dubbed the "comeback kid" for earlier popularity resurgences -- campaigned into the night on Monday, clinging to the outside prospect of an upset in the final two U.S. states to make their selections in the six month primary voting season.

Clinton told voters in South Dakota Monday: "We're going to make our case to all the delegates as to who would be the best president, number one -- because that's the most important question -- and number two, who would be the stronger candidate against John McCain; and I believe on both of those questions I am the person who should get the support to get the nomination for our party."

CNN senior political correspondent Candy Crowley reported that "only a handful of people at the inner core of the Clinton campaign knows what she's thinking about doing when Tuesday's dust settles."

"Those who have been with her since nearly the beginning are saying she will not push this into the convention.

"As one close Clinton supporter put it, she's acutely aware of her place in the party. She will not ruin the party."

All About U.S. Presidential Election • Democratic Party