By Colleen McCain Nelson, Laura Meckler and Peter Nicholas 

MILWAUKEE--Hillary Clinton pressed Bernie Sanders on the viability of his proposals for free health care and college tuition in a Democratic presidential debate Thursday, warning that it is important to level with the American people about what is possible.

The Vermont senator, in response, didn't hesitate to stand by his proposal to impose new taxes on the wealthy and Wall Street to provide those new government services. However, he appeared to have no reply when the former secretary of state pointed out that his education proposal would require Republican governors to spend more money to make it happen.

Mr. Sanders's plan "rests on making sure that governors, like Scott Walker [of Wisconsin], contribute $23 billion on the first day to make college free. I'm a little skeptical," she said, to loud applause.

In a wide-ranging exchange, the first after the candidates split victories in the Iowa caucuses and New Hampshire primary, they agreed with each other more than they disagreed and both appealed to the minority voters who will play a larger role in the next two races, in South Carolina and Nevada.

The debate elicited few surprises and revealed no significant change in tactics by either camp that could shift the dynamics of what appears to be a highly competitive fight for the Democratic Party presidential nomination that is likely not to be resolved for months.

The debate opened with a tense exchange over one of the pair's sharpest policy differences--Mr. Sanders's proposal to create a single-payer health-care system that would replace private insurance with a government-funded system.

Mr. Sanders said it is imperative for the U.S. to guarantee health care as a right, not a privilege. Mrs. Clinton questioned his assertion that a typical American family will see $500 more in taxes while saving $5,000 in health-care costs.

"The numbers don't add up," she said. "That's a promise that cannot be kept."

Mr. Sanders responded by speaking of a general imperative. "Here is the reality, folks. There is one major county on Earth that does not guarantee health care to all people," he said.

Mrs. Clinton replied that the U.S. system is fundamentally different from European countries, which have government systems, and that the Affordable Care Act was meant to build on the employer-based system in place.

Mrs. Clinton suggested that her opponent was promising more than he could deliver as president and would plunge the country back into another protracted debate over health care. "I feel we have to level with people," she said, adding that "we have a special obligation to make clear what we stand for, which is why we should not make promises we can't keep."

She said she has specified what her proposals would cost--$100 billion a year. "Once I'm in the White House, we will have enough political capital" to close tax loopholes and raise taxes on wealthy Americans--steps that would pay for her programs, she said.

In reply, Mr. Sanders seized on her confident prediction that she will be the next president. "Secretary Clinton, you're not in the White House yet," he said. He didn't put a dollar amount on his proposals, which research by The Wall Street Journal suggests would cost about $1.7 trillion a year.

On the issue of race, both candidates pledged to create new opportunities and address inequities.

Mr. Sanders decried a broken criminal justice system that he said allows mass incarcerations and "kids getting arrested." Mrs. Clinton spoke about the challenges African-Americans face and said she would "tackle those barriers that stand in the way of too many Americans" by addressing a wide range of issues, from jobs to criminal justice reform.

Thursday's matchup came on the heels of Mr. Sanders's convincing win in the New Hampshire primary, where he won more women in every age bracket except those 45 years and older.

When asked why she didn't garner broader appeal, Mrs. Clinton demurred. "I have no argument with anyone making up her mind about who to support, " she said. "I just hope that by the end of this campaign, there will be a lot more supporting me."

Mrs. Clinton declined to agree or disagree with the controversial comment from one of her supporters, former Secretary of State Madeleine Albright, who said there was "a special place in hell" for women who don't support one another. She noted instead that her friend had been saying that for many years.

Mr. Sanders was asked if he was worried that he might be standing in the way of a historic achievement: election of the first woman president. He replied that given his background and views--he says he's a democratic socialist--"a Sanders victory would be of some historical accomplishment as well."

The Clinton campaign is counting on states with more diverse electorates to create an election-race firewall that halts Mr. Sanders's rise, but both campaigns are preparing for a prolonged battle, stretching into March and perhaps beyond.

Polls taken before the New Hampshire primary showed Mrs. Clinton with double-digit leads in Nevada and South Carolina, but Mr. Sanders has moved quickly this week to capitalize on his win and build support among minority voters.

Both Democratic contenders have rolled out endorsements from African-American officials and celebrities in recent days. On Thursday, the political arm of Congressional Black Caucus threw their support to Mrs. Clinton, and entertainer Harry Belafonte endorsed Mr. Sanders in a video message.

Mr. Sanders's decisive victory in New Hampshire highlighted the resonance of his call for a political revolution and his argument that a rigged economy is unfairly benefiting Wall Street and the wealthy.

He hit upon those themes again Thursday, saying that his campaign's success was evidence that the American people are tired of establishment politics and establishment economics.

"They want a political revolution in which millions of Americans stand up, come together, not let the Trumps of the world divide us, and say, you know what, in this great country, we need a government that represents all of us, not just a handful of wealthy campaign contributors," Mr. Sanders said.

Write to Colleen McCain Nelson at colleen.nelson@wsj.com, Laura Meckler at laura.meckler@wsj.com and Peter Nicholas at peter.nicholas@wsj.com

(END) Dow Jones Newswires

February 11, 2016 23:11 ET (04:11 GMT)