LOS ANGELES—Facing a backlash from supporters, Barack Obama's campaign reversed course Thursday and reinstated hundreds of people to lists of prospective California delegates for the Democratic National Convention. The campaign's decision this week to block approximately 900 people from trying win seats to the convention as Obama delegates set off a deluge of criticism that reached Web sites, newspaper headlines and party offices, shaking a campaign known for galvanizing the party's grass roots. Campaign manager David Plouffe said in a letter to potential delegates that all names would be restored to ballots that will be used Sunday to elect delegates,...