In some of the tensest moments of the 2020 debates, a viewer might have concluded that Democrats were poised for a large-scale clash over the legacy of President Barack Obama.

There have been heated arguments about whether to stick with Mr. Obama’s architecture for health care policy or to pursue a single-payer system, and flashes of direct criticism over his record on immigration. In televised debates, Democratic rivals like Julián Castro have pressed his former vice president, Joseph R. Biden Jr., to repudiate the large-scale deportations carried out under Mr. Obama’s watch.

There have also been defiant professions of loyalty, delivered as though Mr. Obama were under siege from fellow Democrats. Mr. Biden, the Democratic front-runner, has made these moments a hallmark of his candidacy: “I stand with Barack Obama all eight years, good, bad, indifferent,” he said at the last debate.

Yet among the vast majority of Democratic voters, there is little appetite for a brawl over the merits of Mr. Obama’s record. And while Mr. Obama’s consensus-seeking liberalism appeals to many Democratic voters, few appear to be thinking about the 2020 primary as a forum for determining which candidate would follow Mr. Obama’s exact policy blueprint.