George W. Bush and his team like to deride the critics of their hurricane handling for playing the “blame game” when, in their view, the focus should be on the future. But if anyone is playing that game, it is the White House itself. And the administration doesn’t seem to be winning.

Firing one senior official and having the president issue a somewhat technical acceptance of responsibility seemingly undercuts the intense White House effort to blame Louisiana’s Democratic politicians for the flawed handling of Hurricane Katrina’s deadly impact.

And while the blame game among local, state and federal officials plays out in public, an even more intense search for responsibility goes on behind the scenes in the White House. The most obvious target was Michael D. Brown, ousted last week as the director of the Federal Emergency Management Agency. But the president’s inner circle, while escaping blame in the public debate, should get low marks for a critical decision to keep Bush on the road talking about Iraq and Medicare as Katrina hit. At the time, White House Chief of Staff Andrew H. Card Jr. and Deputy Chief of Staff Karl Rove — also, of course, the president’s senior political adviser — were more concerned about fallout from anti-war protesters than they were about the still-unclear impact of the approaching hurricane.

Sending the president to California for a war speech as Katrina crushed the Gulf Coast is perhaps the single biggest reason that Bush seemed out of sync with the disaster at that early stage. As the levees gave way in New Orleans, the president was way off message.

It is especially surprising that Card, who primarily organizes Bush’s schedule, would have contributed to the administration’s flat-footed image in this way. When the first President Bush drew political heat in 1992 for a slow response to Hurricane Andrew’s devastation of South Florida, he put Card, then the Transportation secretary, in charge of damage control. White House Press Secretary Scott McClellan, when asked about the administration’s role in the crucial 24 hours after New Orleans flooded, gave a typically terse response, although he put the responsibility squarely on Card’s shoulders. “Andy Card is the chief of staff, and he was in close contact with everyone,” McClellan said in a Sept. 6 news briefing.

Once the extent of the disaster was clear, Card and Rove got into gear very quickly. They reordered the president’s schedule, cut short his vacation and sent him to the Gulf Coast several times. They also got their supporters and friends in the conservative news media to start blaming Louisiana’s local and state officials, who are mostly Democrats.

But they were not the first to try to shift blame in this debate. New Orleans Mayor C. Ray Nagin and other Louisiana officials started the Katrina blame game as soon as the storm’s disastrous effects were becoming clear. “Where’s the cavalry?” they repeatedly asked, referring to the federal assistance they were expecting. That shifting of responsibility worked initially, but — thanks to prompting from the White House — the national debate eventually got around to examining the state and local governments’ failings as well.

Still, it was two surprising moves by the White House itself that may ultimately pin the blame on the administration, although Card and Rove may have a potentially workable strategy for avoiding it.

First, Brown was dismissed. Bush does not like to fire people because he is so loyal to his workers, according to White House spin. But there is another reason, say some who are close to the president: A firing in the face of criticism looks like an admission of error, Bush believes.

But in the most surprising development of all, Bush actually admitted error, sort of. “To the extent that the federal government didn’t fully do its job right, I take responsibility,” he said last week.

The firing and the mea culpa will test whether Bush’s longstanding reluctance to make such moves is justified. If so, he might decide to get rid of some others and to issue more statements of remorse.

But Card and Rove are surely hoping for another consequence, which is now in play. Firing Brown freed the loyal Bush aide to go forth as a private citizen and reinforce the White House blame game. Although “Brownie” dinged the president’s top deputies, including Card, in an interview with The New York Times published Sept. 15, implying that his early warnings of chaos on the ground went unheeded, he absolved the White House of fault and instead blamed Louisiana Gov. Kathleen Babineaux Blanco, a Democrat.

Because nobody plays the blame game better than this crowd, the president’s carefully worded acceptance of responsibility might serve to quiet the hounds long enough to get this story behind them. But Katrina was huge, and still might prove to be more than even the best-disciplined White House can handle.

Contributing Editor Craig Crawford is a news analyst for MSNBC, CNBC and “The Early Show” on CBS. His new book is “Attack The Messenger: How Politicians Turn You Against The News Media.”