"It was the moment she retook the reins of this race and showed women and men why she is the best choice," said Howard Wolfson.
Obama's team pointed to another part of the debate as his signal moment.
Clinton was criticizing Obama's legislative record.
"I have to confess, I was somewhat amused the other night, when, on one of the TV shows, one of Sen. Obama's supporters was asked to name one accomplishment of Sen. Obama and he couldn't," Clinton said.
In response, Obama listed some of the legislation he had backed and then hammered his message — referring to the movement his candidacy has spawned.
"I do think there is a fundamental difference between us in terms of how change comes about," he said. "Sen. Clinton of late has said, 'Let's get real.' The implication is that the people who've been voting for me or involved in my campaign are somehow delusional."
"Well, I think they perceive reality of what's going on in Washington very clearly," he added. "What they see is that if we don't bring the country together, stop the endless bickering, actually focus on solutions and reduce the special interests that have dominated Washington, then we will not get anything done. And [that is] the reason that this campaign has done so well."
If voters came looking for major policy distinctions or an all-out brawl at the University of Texas, they might have left disappointed.
The first 20 minutes of the debate were so civil, it almost seemed like there were no differences between the two candidates' positions.
After one question about a fence along the U.S. border with Mexico — which Clinton said she would look for new technologies and "smart fencing" instead of a physical barrier — Obama responded by saying, "Well, this is an area where Sen. Clinton and I almost entirely agree."
But there were a few choice encounters.
After a questioner asked about Obama borrowing phrases from Massachusetts Gov. Deval Patrick, Clinton pounced.
"You know, lifting whole passages from someone else's speeches is not change you can believe in, it's change you can Xerox," she said as the audience booed loudly.
She pressed on: "If you look at the YouTube of these videos, it does raise questions."
There was a lot of discussion about immigration reform in this heavily Latino state, in a debate co-sponsored by the Univision network.
Perhaps appealing to those Hispanic voters, Clinton for the first time said she would push for comprehensive immigration reform within her first 100 days.
"We need a path to legalization," she said, "to bring the immigrants out of the shadows, give them the conditions that we expect them to meet, paying a fine for coming here illegally, trying to pay back taxes over time, and learning English. If they had a committed a crime in our country or the country they came from, then they should be deported. But for everyone else, there must be a path to legalization. I would introduce that in the first 100 days of my presidency."
Obama and Clinton discussed their differences on health care at length. And on the prospect of a new leader in Cuba, the candidates differed once again on whether it is appropriate for a president to meet with regimes with whom the United States does not have diplomatic relations.