BP and Halliburton will not go out from negative publicity. Especially in the case of Halliburton, who goes down to the local corner Halliburton store and buys a barrel of oil? No one. Their customer base isn't the public, directly anyway. People can get gas at BP stations, but those are a small part of their business.
Does anyone happen to know what happened to Exxon after Exxon-Valdez?