The relation between President Obama's words and Hillary Clinton's campaign is not immediately clear but is real nonetheless.
Steve M. quotes The New York Times quoting Robert Reich saying of Hillary Clinton "If she’s going to get anything done as president, she is going to have to have a mandate.” Recognizing that Democrats are best served by running up the score and thereby possibly winning a congressional majority, SM. explains
if Republicans don't have this excuse for blocking all her initiatives, they'll found some other excuse. They'll say they held the House and Senate, or held the House and nearly held the Senate, therefore Americans voted for divided government, and want them to be a check on her radical socialist big-government policies. Or they'll just do what they did in 2009 and 2010: they'll block everything just because they can, and offer no explanation, or say, as they said with Obama, that Clinton campaigned as a healer and then decided to govern as an ideologue, even if this is blatantly contrary to the evidence....
Republicans will never, ever grant that Clinton has a mandate. If the candidate had been Sanders and he'd won in a blowout with an unabashedly ideological, issue-oriented campaign, they wouldn't have granted that he had a mandate. They just don't do that. No election outcome will prevent them from standing athwart history yelling "Stop."
That's a pretty safe bet. Republicans simply have no reason not to say "no!" to President Clinton's modest proposals, propose a radical, extremist agenda in response, then wait for the mainstream media to demand a compromise. We know that. We've had eight years observing it.
But Steve M. fails to acknowledge that Obama never did claim a mandate. Consider Barack Obama's inaugural address in 2008, when, feeling the bipartisan spirit, he declared "The question we ask today is not whether our government is too big or too small, but whether it works."
Upon accepting the Democratic nomination for President in 1988, Michael Dukakis had stated "This election isn't about ideology; it's about competence" and once he lost, we all laughed. When Obama rephrased it in 2008, we applauded. However, a week before Obama's second inaugural address, The Nation's John Nichols wrote
After a 2012 election campaign that his Republican foes portrayed as a referendum on the role of government, Obama has a mandate to make government work again for the American people. His inaugural address should claim that mandate with all the passion and all the determination that FDR brought to the mission seventy-six years ago.
The President responded with
Being true to our founding documents does not require us to agree on every contour of life. It does not mean we all define liberty in exactly the same way or follow the same precise path to happiness. Progress does not compel us to settle centuries-long debates about the role of government for all time, but it does require us to act in our time.
That was weak tea, steeped for about 20 seconds, and an acknowledgment that we do not have "to agree on every contour of life" could have served as a metaphor for a pragmatic, centist president who chose not to claim a mandate.
Steve M. probably is right that Hillary Clinton, even if she were to win in a landslide, could not claim a mandate Republicans wouldn't disregard and ignore. It is, nonethless, speculation, for we don't have recent experience with a Democrat claiming a mandate. We have only one who elected not to impose any but the most modest reforms on a nation, and progressive allies who barely raised a peep of protest.