Obama Or Carter?

Marc cites CNN's Ed Henry:

While the words Barack Obama were never used White House aides privately admit the President referring not just to Barack Obama but other Democrats like Jimmy Carter, for example, who has recently suggested himself has sat down with Hamas leaders and has suggested that the U.S. government to should sit down with Hamas. So, the inference is clear. Although the President didn't name names, administration officials are privately acknowledging this was a shot at Barack Obama and other Democrats.

Gillespie, meanwhile, said that Bush was aiming at Carter and not Obama. Which is it?