I was covering his remarks and there wasn’t much reaction from the room at the time. But by the next morning, tweets were flying, a hashtag had been created — people proudly proclaimed they were #TooFarLeft — and voters, activists and strategists were chattering.

And, boy, did they have plenty to say. Mr. Obama got a resounding chorus of “O.K. boomer” from liberal activists, who questioned his record on issues like health care, climate change and immigration…

People close to the former president say he wasn’t bothered by the reaction. At this point in his life, he feels liberated to give what he sees as his best advice to his fellow Democrats based on his political experiences.

And he’s giving voice to concerns from moderates that have been bubbling up for several weeks now as Ms. Warren and Mr. Sanders have shown resilience in the polls. But Mr. Obama’s sentiments are in direct conflict with what the more liberal activists who have an outsize role in the party’s politics and the nominating process have been expressing.