Obama, riding a crest of support from young voters, said, "Words do inspire, words do help people get involved ... Don't discount that power."
Clinton sharply criticized Obama's health care plan and accused him of flip-flopping on several campaign promises he made when running for the Senate in 2004, including pledges to vote against the Patriot Act and Iraq War funding.
"Sen. Obama can have a pretty good debate with himself," said Clinton, whose campaign sent out a flyer Saturday questioning his commitment to abortion rights, citing some of his votes in the Illinois State Senate.
"We don't need to be raising the false hopes of our country about what can be delivered," she said, adding, "I think I am the agent of change I embody change. I think having the first woman president is a huge change."
Obama, who took his share of shots at Clinton before his Iowa win, remained composed under her attacks, telling her, "I think it's important what we don't do is to distort each other's records."
John Edwards, buoyed by his second-place Iowa finish, defended Obama as his partner against the Clinton-led "status quo," saying, "I didn't hear these kinds of attacks from Sen. Clinton when she was ahead."
But it was New Mexico Gov. Bill Richardson, the fourth and final candidate invited to the ABC News/Facebook debate, who probably had the best line of the night: "I've been in hostage negotiations that were a lot more civil than this."
When the moderator asked Clinton why many voters perceive her as less likeable than Obama, she joked, "That hurts my feelings, but I'll try to go on He's very likeable. I don't think I'm that bad."
The Illinois senator chimed in with, "You're likeable enough."
Obama's stunning win in Iowa hasn't apparently translated into a huge bump in the polls comparable to the 17-point rise that buoyed John Kerry when he defeated Howard Dean in 2004. The Illinois Democrat pulled into a 33-percent-to-33 percent tie with Clinton, according to a CNN/WMUR survey taken over the last two days, a modest 3-point increase over a poll taken at the end of December. Clinton lost only a single point, according to the poll, which had a 5-percent margin of error.
Edwards also picked up three points, rising to a strong third place with 20 percent.
Clinton's team engaged in an internal struggle over how and when to go negative on Obama. The campaign shelved plans to air negative TV ads Friday but sent mailed an anti-Obama pamphlet that him for voting "present" -- not yes or no -- on seven bills relating to a woman's right to choose. Obama says he favors abortion rights.
"A woman's right to choose demands a leader who will stand up and protect it," the mailing reads.
Obama says his neutral votes were part of a legislative strategy approved by pro-abortion-rights groups.
Earlier in the day, Obama hosted a morning rally at Nashua North High School that appeared to spell trouble Clinton.
While she was 40 miles away, addressing a crowd of 800 people at Merrimack Valley High School, 2,800 people waited in a line stretching a quarter mile from the school, braving freezing temperatures for as long as two hours.