Though they rarely mention the president by name or address his policies, Labor Secretary Tom Perez and Minnesota Rep. Keith Ellison have sent a clear message that Mr. Obama has left the party in a weakened state.

Messers. Perez and Ellison—along with state chairmen Jaime Harrison of South Carolina and Ray Buckley of New Hampshire, who are also candidates for chairman of the DNC, are seeking a mandate to reverse Obama-era tactics that cut funding and attention to local parties and left Democrats with far less power in Congress, governorships and state legislatures than when his presidency began.