Does Clinton's gay marriage support mean 2016 run?

(CBS News) Former Secretary of State Hillary Clinton formally announced her support for same-sex marriageon Monday, releasing a video she made with the Human Rights Campaign in which she insists that gays and lesbians are "full and equal citizens and deserve the rights of citizenship."

The Human Rights Campaign said Clinton approached the organization about recording the statement and a Clinton spokesperson called the timing "natural" given that two gay marriage cases will come before the Supreme Court next week.

Throughout the nearly six-minute video, there were several references to unfinished work and an ongoing journey, prompting increased speculation that Clinton will consider a 2016 presidential run, a possibility she has continually downplayed since her departure from public office earlier this year.

In a January interview, Clinton told National Public Radio, "I don't see myself getting back into politics. I want to be involved in philanthropy, advocacy, working on issues like women and girls that I care deeply about."

Still, many have compared the look and tone of the recent Human Rights Campaign video to the 2007 video in which Clinton launched her 2008 presidential campaign. And 2016-watchers note that in the last month, Clinton has relaunched her website and has said she is working on a book about her time as secretary of state.

The speculation puts Clinton in line with other possible Democratic presidential contenders, including Vice President Joe Biden, New York Governor Andrew Cuomo, and Maryland Governor Martin O'Malley.

But on Sunday, David Plouffe, a former top adviser to President Obama, said Clinton would be the candidate to beat in 2016.

"It's too soon to know. I think she is, in both parties right now, by far I think the most interesting candidate, probably the strongest candidate," Plouffe said.

For more from CBS News' Jan Crawford on Hillary Clinton's presidential aspirations, watch her full report above.