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Mr Obama shook his head and dismissed the charge, before saying: "What we shouldn't be spending time doing is tearing each other down. We should be spending time lifting the country up."
He went on: "Senator Clinton of late has said, 'Let's get real,'" he said. "The implication is that the people who've been voting for me or involved in my campaign are somehow delusional."
He pointed out that those suffering from such delusions would include "the 20 million people who've been paying attention to 19 debates and the editorial boards all across the country at newspapers who have given me endorsements - including every major newspaper here in the state of Texas".
The debate began with milder disagreements clashes over the significance of Fidel Castro's resignation as Cuban president. Asked if they would be willing to meet the island nation's new leader without preconditions, Mrs Clinton said she would not, while Mr Obama said he would.
But Mrs Clinton, who has tried hard over recent days to underline her credentials as a prospective president and commander-in-chief, found Mr Obama agreeing with her on most substantive policy areas examined last night - including immigration which is a key issue for Latino voters in Texas.
One area where they clashed sharply was over their respective plans for reforming health care. Mrs Clinton once more claimed Mr Obama's proposal - which does not require people to buy insurance - would leave 15 million people without cover.
"If you do not have a plan that starts out attempting to achieve universal health care, you will be nibbled to death, and we will be back here with more and more people uninsured and rising costs," she said.
Mr Obama hit back by criticising his rival for the way she had managed efforts 14 years ago to change the system. "Senator Clinton and the administration went behind closed doors, excluded the participation even of Democratic members of Congress who had slightly different ideas than the ones that [she] had put forward," he said. "And, as a consequence, it was much more difficult to get Congress to cooperate - I'm going to do things differently."
They were later asked how they would tackle John McCain as the likely Republican nominee in a November general election. Mr Obama said that his opposition to the war in Iraq would give him an advantage.
"It is going to be much easier for the candidate who was opposed to invading Iraq in the first place...In the single most important decision of our generation, the war in Iraq, I think I showed the judgment of a commander in chief and I think Senator Clinton was wrong in her judgment," he said.
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