That left Obama with an overall lead of 101 delegates, 1,562-1,461 as the rivals look ahead to the final dozen contests on the calendar. It takes 2,025 to win the nomination.
The two presidential contenders made the rounds of the morning television news shows, agreeing on little - except that their historic struggle would continue at least until the Pennsylvania primary on April 22.
That left six weeks for public campaigning, and for private appeals to party leaders, known as superdelegates, who attend the convention but are not chosen in primaries or caucuses.
Clinton has the support of 241 superdelegates, and Obama 202. But more than 350 remain uncommitted, a large enough bloc to swing the nomination should they band together.
Clinton, in particular, projected confidence on the day after her candidacy-saving victories, suggesting she might want Obama as her vice presidential running mate.
"That may be where this is headed, but of course we have to decide who is on the top of ticket. I think the people of Ohio very clearly said that it should be me," she said on CBS.
Obama brushed such talk aside. "We are just focused on winning this nomination," he told reporters aboard his chartered campaign jet en route to Chicago from Texas.
He said he would prevail in the nominating battle despite facing a tenacious candidate who "just keeps on ticking."
Democrats plunged into the next round of their campaign as Republican John McCain visited the White House to confirm his status as the party's nominee-in-waiting. Lunch with President Bush - and an endorsement - headlined his day.
Bitter rivals in the 2000 presidential primaries, the two have forged an uneasy relationship during Bush's administration and have clashed on issues such as campaign finance, tax cuts, global warming and defining torture.
There were 370 Democratic delegates at stake in Tuesday's contests, and nearly complete returns showed Clinton outpaced Obama in Ohio, 74-65, in Rhode Island, 13-8, and in the Texas primary, 65-61.
Obama won in Vermont, 9-6, and was ahead in the Texas caucuses, 30-27. Ten of the dozen that remained to be awarded were in Texas; the other two in Ohio.
"We still have an insurmountable lead," Obama said.
Clinton and Obama spent most of the past two weeks in Ohio and Texas in a bruising campaign, with the former first lady questioning his sincerity in opposing the North American Free Trade Agreement and darkly hinting he's not ready to be commander in chief in a crisis.
Based on their current delegate counts, neither candidate can win enough delegates in the remaining primaries and caucuses to secure the nomination without the help of nearly 800 party officials and top elected officials who also have a voice in the selection. On Wednesday, Clinton and her campaign clearly aimed their case at those so-called "superdelegates" - a strategy that could take the nomination fight all the way to the party's August national convention in Denver.
"New questions are being raised, new challenges are being put to my opponent," she said. "Superdelegates are supposed to take all that information on board and they are supposed to be exercising the judgment that people would have exercised if this information and challenges had been available several months ago."
She said voters are being drawn to her argument that she would be the better commander in chief, the best steward of the economy and that she can better confront McCain in the general election.
Obama countered that on a key national security issue - the war in Iraq - "she got it wrong" by supporting Bush's call for authority to use military force.
As for superdelegates, Obama said he expected them to rally around him.
"I don't think it will necessarily go to the convention floor," he told reporters aboard his plane before taking off from San Antonio for Chicago.
He also said he will challenge Clinton on her foreign policy credentials.
"Was she negotiating treaties? Was she handling crises? The answer is no," he said. "She made a series of arguments on why she should be a superior candidate. I think it's important to examine that argument."
The count does not include delegates from Florida and Michigan, who were penalized by the Democratic Party for moving up their primaries ahead of a schedule set by the Democratic National Committee. None of the Democratic candidates campaigned in either state. But Clinton, who won the popular vote in both state primaries, on Wednesday renewed her call for Florida and Michigan to be counted in the nomination race.
"It's a mistake for the Democratic Party to punish these two states," she said. "I don't see how a Democratic nominee goes forward alienating two of the most important states."
McCain surpassed the 1,191 delegates needed to win his party's nomination against odds that seemed steep only a few months ago, and all but impossible last summer.
Facing 5.
Mike Huckabee hung in until Tuesday night, gamely keeping up the fight weeks after dropping from long shot to afterthought.
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Associated Press Writer Tom Raum in San Antonio
