Obama and Biden’s Relationship Looks Rosy. It Wasn’t Always That Simple.

“You are the pick of my heart, but Joe is the pick of my head,” Mr. Obama told Mr. Kaine after he made his choice, according to people with knowledge of the exchange.

Eleven years later, Mr. Obama’s cautions and calculations have come to roost.

Mr. Obama, standard-bearer of change but conscious of the racial dynamics of his candidacy, was wary of asking voters to digest too much at once. In Mr. Biden, he found a running mate who would conjure the comforting past and provide experience he did not possess, but would not maneuver for the presidency from the No. 2 slot.

While Mr. Biden exceeded the first two expectations, he never abandoned his aspirations for the top job. He has leveraged his steady vice presidency into a fragile front-runner status in the 2020 primary, at the even more advanced, and politically vulnerable, age of 76.

What’s more, the choice of Mr. Biden as a hedge against change has left the demographically and ideologically evolving Democrats profoundly divided as they desperately seek to unseat President Trump. Even as Mr. Biden casts himself as the man to complete and cement the Obama legacy, that legacy has moved to the center of the Democrats’ fractious debate.

While paying homage to Mr. Obama, who remains popular among Democratic voters, many candidates, including Senators Elizabeth Warren, Bernie Sanders, Kamala Harris and Cory Booker, are urging the party to move far beyond his administration’s positions on immigration, criminal justice, health care, the regulation of banks, the environment, income inequality and race, which they now view as timid, conservative or dated.