While I find it a bit unorthodox to have the President ask a CEO to step down, this was a needed step towards fixing GM. The believed next in the line is GM's COO Fritz Henderson, although the position may be filled by someone from outside the company.
I believe that the best bet would be to hire from outside the company. Usually, I am not a big fan of hiring from outside a company, as I am a strong believer that the people who work their way up through a company deserve the first look when a promotion becomes available. However, in this instance, GM has made too many mistakes to rely on someone within. The risk is that the new CEO would possibly continue the previous policies or have loyalties to parties that may not result in the best interest of the company.
According to the Bloomberg story, the government will be responsible for determining a replacement. They also report that Obama plans to give a speech tomorrow about the future of the automotive industry. Check in tomorrow for my take on Obama's plan.