Mrs. Clinton also said that if she could not generate the money needed to pay for universal coverage through other means, she would not object to raising the excise tax on tobacco products, which Congress last increased in 1997 to 39 cents a pack.

Image Senator Hillary Rodham Clinton being interviewed about what her universal health care program would look like. Credit... Damon Winter/The New York Times

“I’m a big believer in raising tobacco taxes,” Mrs. Clinton said when asked whether an increase should be on the table. “You know, when we were working on the Children’s Health Insurance Program, that’s the funding stream that the Congress came up with, which was bipartisan, which worked out very well. At some point, there’s going to be diminishing returns. But, sure, why not? I don’t have any objection to that.”

As in her debates with Mr. Obama and other contenders, Mrs. Clinton displayed an easy command of health policy in the 45-minute interview, conducted in a basement meeting room in the Midtown Manhattan tower that houses her Senate office. Her voice hoarse, she conceded some weariness from the lengthy campaign, saying her decision to take off the Easter weekend had only allowed exhaustion to set in. But despite calls by some Democrats for her to abandon the race, she gave no hint that she was viewing her campaign in the past tense.

Mrs. Clinton presented a confident defense of her call for universal coverage, saying it reflected not only a moral imperative, but also the best chance to reduce costs and improve quality.

“I know that there are a lot of experts who may disagree about how to get to universal health care,” she said. “But they agree with me that in the absence of universal health care it’s very difficult to control costs, and it’s extremely hard to incentivize quality improvements at the level you need to really see results.”

Though that view is not shared by Senator John McCain or any of the rivals he vanquished to secure the Republican nomination, Mrs. Clinton said she thought that “the time is right” to build a bipartisan consensus to reorganize the health system.