WASHINGTON (CNN) -- After Thursday's Senate Judiciary Committee hearing, several administration officials tell CNN they believe the attorney general should and may be convinced to step down.

They agree that Thursday's testimony did not do much to help Gonzales regain credibility on Capitol Hill and in fact, may have lost some of the few supporters he had left.

Several noted Gonzales' close relationship with the president as a wild card in this equation -- citing the president's loyalty. They said the president believes Gonzales did not do anything wrong and suggest he is not eager to give in to demands from Congress, especially when it involves one of his close confidants.

They said they believe President Bush's aides may try to get Gonzales to realize staying on will not help the [resident move his agenda forward. They insisted they do not think the president will ask Gonzales to step down.

One official who works closely with Gonzales said that the attorney general is still optimistic and still believes he can remedy the situation. This official described Gonzales as "out of touch" with the political pulse in Washington.

Several officials said that discussions have begun in Republican circles about a possible replacement. One name that consistently comes up is Ted Olson, former Solicitor General. Olson is seen as having the experience, reputation and credibility it would take to steer the department for the next year and a half.