Democrats in South Dakota and Montana cast the final votes in a grueling battle for the right to face Republican John McCain in November's presidential election, with 31 delegates to the August convention in Denver at stake.
Obama is within about 40 delegates of the 2,118 he needs to capture the nomination and become the first black nominee of a major U.S. political party.
He could hit that number as soon as Tuesday night depending on how quickly he wins commitments from nearly 200 uncommitted superdelegates -- party officials who are free to back any candidate.
"There are a lot of superdelegates who are waiting for the last couple of contests but I think that they are going to be making decisions fairly quickly after that," Obama told reporters in Michigan on Monday.
U.S. Rep. James Clyburn of South Carolina, the third-ranking Democrat in the U.S. House of Representatives and the top-ranking black member of Congress, backed Obama on Tuesday morning.
"Today the process ends," Clyburn told NBC's "Today" show.
Other House members were expected to follow his lead, party sources said.
Voting ends in South Dakota at 7 p.m. MDT/9 p.m. EDT (0100 GMT), and in Montana an hour later, with results expected shortly after.
Clinton and her campaign sent mixed signals on Monday about how long she would stay in a presidential race that she began as a heavy favorite but now has little chance of winning.
Campaigning in South Dakota, Clinton said the end of the voting marked "the beginning of a new phase of the campaign" in which she will plead her case to superdelegates that she would be the strongest candidate against McCain in November.
"The decision will fall to the delegates empowered to vote at the Democratic convention. I will be spending the coming days making my case to those delegates," she told supporters in Yankton, South Dakota.
But her husband, former President Bill Clinton, sounded like he was counting down the hours at a campaign stop in South Dakota on Monday. "This may be the last day I'm ever involved in a campaign of this kind," he said.
One of Clinton's top supporters, Gov. Ed Rendell of Pennsylvania, told CNN he expected her to spend Wednesday and Thursday making her pitch to superdelegates.
'OBAMA TO GET DELEGATES HE NEEDS'
"I don't think it's going to prevail, to be candid," he said. "Senator Obama is going to get the delegates he needs certainly by the end of the week, then I think Senator Clinton is going to do the right thing and move fairly decisively to unify the party and we will all follow her lead."
With no more campaign trips to plan, workers who handle Clinton's advance travel arrangements have been told to go to New York or head home until further notice, aides said.
Obama plans a victory celebration to kick-off the general-election campaign against McCain after the South Dakota and Montana polls close on Tuesday night. He will hold it at the Xcel Energy Center in St. Paul, Minnesota -- the site of the Republican convention in September.
The Obama campaign has been urging superdelegates to make their endorsement before the voting ends on Tuesday, so the delegates he wins in the two states can put him over the top in the Democratic race.
A group of 17 uncommitted Senate Democrats met on Monday to discuss a potential endorsement of Obama. Many are poised to announce either on Tuesday or wait another day to give Clinton a chance to bow out, Senate aides said.
Both Obama and Clinton will speak to a pro-Israeli lobbying group in Washington on Wednesday, and Obama said he expected to be talking to Clinton again soon.
He said he told her in a phone conversation on Sunday that "once the dust settled I was looking forward to meeting with her at a time and place of her choosing."
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