It's that simple. Obama doesn't give a damn what happens in Iraq, and he never has, which is why he still can't give Bush credit for the troop surge that tamped down violence to this point. His sole comment on Bush was a defensive one -- Bush was a patriot who supported the war, and Obama is a patriot who opposed it.
Obama can't thank Bush because Obama was going to pull out regardless of the consequences. From Obama's perspective, he has nothing to thank Bush for. If Obama had gotten his way and the surge had been shelved, Iraq would have devolved into chaos -- and Obama would have pulled out American troops. If Obama didn't get his way, and the violence was tamped down -- well then, Obama still would have pulled out American troops.
That is always Obama's goal: Pulling out American troops, no matter what is left in the wake. Which is why he's pursuing exactly the same strategy in Afghanistan, the so-called "war of necessity" -- we may need to be there, according to Obama, but not as much as he needs to get American troops out of there before the beginning of his re-election campaign. This pleases the America-last press enormously, and so they treat Obama's Bush-lite rhetoric with kid gloves.
While Obama and Bush may differ on principle -- Bush actually believed it was a worthy goal to free Iraq and make her an ally of the United States while killing vast scores of terrorists; Obama believes that the only worthy military goal is cutting the defense budget -- they will share the burden of history when it comes to Iraq.
Bush had to carry the weight of his "mission accomplished" speech for the rest of his presidency, but he emerged victorious after finally hitting upon the strategy that solidified the country. Obama will have to carry the weight of his "mission accomplished" speech, too -- only Obama's utter disregard for Iraq's future will put the lie to his own statements.
"When the history books are written," Bush said shortly before leaving office, "they will show that freedom prevailed." History will be kind to George W. Bush when it comes to Iraq. It will not be nearly as kind to the man who took his place, but couldn't replace his strength of spirit.