WASHINGTON (CNN) — Sen. Barack Obama has clinched the Democratic nomination for president, according to CNN estimates, making him the first African-American in U.S. history to lead a major-party ticket.

Obama picked up a slew of superdelegate endorsements on Tuesday. Those endorsements, combined with the delegates he’s projected to receive from South Dakota’s primary, will put him past the 2,118 threshold, according to CNN estimates.

Obama will claim victory during a speech in St. Paul, Minnesota, according to prepared remarks released by his campaign.

“Tonight, I can stand before you and say that I will be the Democratic nominee for President of the United States,” he’s expected to say.

His remaining rival, Sen. Hillary Clinton, does not plan to concede the race Tuesday night, campaign chairman Terry McAuliffe told CNN — but one of her leading supporters said “a moment of truth” was at hand.

“I think a decision has to be made about whether keeping this nomination wide open is in the best interest of winning in November,” said Sen. Dianne Feinstein, D-California.

“I do not believe that it is, and I’m a very strong supporter of Hillary being placed on ticket as a vice presidential candidate.”

Two New York lawmakers told CNN on Tuesday that Clinton expressed willingness during a conference call to serve as Obama’s running mate in November.

One of the lawmakers said Clinton’s husband, former President Bill Clinton, has been pushing the idea privately for several weeks. And earlier, Rep. Charles Rangel, D-New York, told CNN, “I have reason to believe she is open to the V.P. slot.”

But in a statement issued Tuesday afternoon, her campaign said there was nothing new in her remarks.

“Today on a conference call with New York legislators, Sen. Clinton was asked whether she was open to the idea of running as vice president and repeated what she has said before: She would do whatever she could to ensure that Democrats take the White House back and defeat John McCain,” the former first lady’s campaign said in a written statement Tuesday afternoon.

Even though she discussed being Obama’s running mate, McAuliffe earlier in the day said Clinton was “absolutely not” prepared to concede the race after the polls close tonight in Montana and South Dakota, the final two contests on the primary calendar.

McAuliffe rejected as “100 percent” incorrect an Associated Press report that Clinton is preparing to acknowledge Obama has the delegates to win the nomination Tuesday night as the five-month Democratic primary process comes to a close.

Former President Jimmy Carter and Rep. James Clyburn, the No. 3 Democrat in the House and the highest ranking African-American in Congress, were two of the most prominent superdelegate endorsements that Obama picked up.

“I came to that decision because I do believe that he has elevated this campaign,” Clyburn said. “He has energized our constituents. He is redrawing an electoral map for Democrats.”

Obama is holding a rally at the Xcel Energy Center in St. Paul, the same arena which will house the 2008 Republican National Convention in September. Clinton will spend the evening at a campaign event in New York City. iReport.com: See what cartoonists think of the interminable race

Obama is looking more and more toward a likely general election matchup with John McCain, the presumptive GOP presidential nominee. Obama has started looking at Clinton as less of a rival and more as an important ally who can help him win in November.

“We’re getting very close to the number that will, that will give us the nomination and if we’ve hit that number on Tuesday night, then we will. We will announce that and I think even if we don’t, this is the end of the primary season, and I think it’s very important for us to focus on the clear contrast that’s going to exist between Democrats and Republicans in this election,” Obama said this weekend while campaigning in South Dakota.

“Sen. Clinton is an outstanding public servant, she has worked tirelessly on this campaign, she has been a great senator for the state of New York and she is going to be a great asset when we go into November to make sure that we defeat the Republicans,” Obama said on the campaign trail Sunday in South Dakota, adding Monday in Michigan that “she and I will be working together.”