Speech in Florida could herald a core theme if she decides to run in 2016 presidential campaign

In an expansive speech in Coral Gables, Florida, last Wednesday, Hillary Clinton said the path for US renewal lies in broadening the participation of women, the poor, young people and other disadvantaged people in the public debate.

Clinton framed an argument for inclusion and equality that could become a core theme of her 2016 presidential campaign, should she decide to run. She recalled one of the formative experiences of her youth, going to hear the Rev Martin Luther King Jr speak on a cold night in Chicago, and said his message still resonates in the 21st century. "I sat on the edge of my seat as this preacher challenged us to participate in the cause of justice, not to slumber while the world changed around us," she recalled.

In her address at the University of Miami, Clinton said the nation's future depends on whether it embraces the idea of "full participation".

"It is the work of this century to complete the unfinished business of making sure that every girl and boy, that every woman and man, lives in societies that respect their rights no matter who they are, respects their potential and their talents, gives them the opportunities that every human being deserves – no matter where you were born, no matter the colour of your skin, no matter your religion, your ethnicity or whom you love," she said.

Clinton began her remarks by commending Arizona governor Jan Brewer for vetoing anti-gay legislation that Clinton called "discriminatory". Clinton said Brewer recognised that "inclusive leadership is really what the 21st century is all about".

Clinton, who served under President Barack Obama as secretary of state and championed healthcare reform in the 1990s, delivered a strong defence of Obama's Affordable Care Act and urged young people in the audience to sign up for health coverage.

"You can't sit here today and tell me for sure you won't have a car accident, you won't have a slip or a fall, you won't have some kind of disease that you never thought you would ever be stricken by," she said. "You just don't know – nobody knows."

Clinton earlier endorsed efforts to change some provisions that have become problematic, such as the employee coverage requirement that has led some US small businesses to move employees from full-time work to part-time work to avoid paying for their healthcare, according to CNN.

"I think we are on the right track in many respects, but I would be the first to say if things aren't working, then we need people of good faith to come together and make evidence-based changes," Clinton said in a keynote address to the Healthcare Information and Management Systems Society's annual meeting, in Orlando.

In her University of Miami appearance, Clinton said the country needs to get beyond the "partisanship" and "political dead-ends" and have what the French political philosopher Alexis de Tocqueville observed in the 19th-century US as "the habits of the heart".

"Equality in itself means nothing unless it leads to opportunities, but those opportunities don't just happen by themselves," Clinton said. "They have to be midwifed. They have to be carefully established and nurtured and spread."

Clinton spoke at the invitation of University of Miami president Donna Shalala, a long-time Clinton friend who served as health secretary under President Bill Clinton. Hillary Clinton typically commands $200,000 or more per speaking appearance, but Shalala told reporters that Clinton agreed to a "highly discounted" fee. Shalala said a university donor covered the costs, but declined to identify the donor.

Shalala asked Clinton a series of questions from students, including one about the continuing turmoil in Syria. Clinton said the international community needs to stay focused on getting chemical weapons stocks out of Syria, adding that more pressure must be brought on President Bashar al-Assad's regime to "finish the job".

Shalala read a question from one student who found a clever way to ask Clinton whether she would run again for president – could Clinton offer any insight about the "TBD …" portion of her Twitter biography.

The arena crowd burst into applause, but Clinton kept her followers guessing. "I will certainly ponder that," she said, smiling.

This article appeared in Guardian Weekly, which incorporates material from the Washington Post