Mr. Augenbraum declined to explain how the mistake was made, saying that it was "an internal question".
Republicans, flushed with victory in the recent mid-term elections, expressed fury even before the announcement was made, saying it would hinder bipartisan co-operation on other topics when they take control of Congress in January.
Mr. Steitz, the NASA spokesman, said the agency might have to improve internal communications, but he defended the way the change was made, saying it reflected the management style of Michael D. Griffin, the administrator at the agency.
Students on both sides of the debate have criticized school officials for what they perceived as the furtive manner in which the decision was made, saying it was not in keeping with the inclusive Quaker tradition of the school.
Romney blasted the deal as soon as it was made, saying it "opens the door to higher taxes and puts defense cuts on the table". Indeed, on NBC's "Meet The Press" on Sunday, Romney in effect criticized his running mate by saying the deal was "a big mistake" by Republican leaders.
Mr. Koch, who attended the January meeting with the Greens, as well as Mr. Richardson, denied that any such offer was made, saying the request for help came from the Greens and that the party offered not to run a candidate.
