The Clinton and Obama worlds continue to collide.

Patti Solis Doyle, fired as Sen. Hillary Rodham Clinton's campaign manager, started her job last week as chief of staff to Obama's yet-to-be-named vice presidential pick. And Neera Tanden, Clinton's policy czar, is joining the Obama campaign as the head of domestic policy.

Now the presumptive nominee hopes to snag John Podesta, Bill Clinton's former White House chief of staff...