McCain’s strategic error

John McCain, recently announced US presidential candidate, has long supported a stronger US force in Iraq, and recently endorsed George Bush’s surge.
If the surge fails, McCain gets tagged with its failure. If it succeeds he can claim credit.
With enough troops and military resources, certainly Iraq (or even Baghdad) could be calmed – there are only 27 million people in Iraq, surely an equivalent force (less than 10 percent of the US population) would bring about peace pretty quickly, however, that number is more than the US and its allies are likely to commit for this cause.
That said, it is unlikely that an extra 21,000 troops are sufficient. McCain had supported more troops before Bush endorse a mere 21,000 troops for the surge.
McCain would have been able to claim the high ground either way had he said we need a surge, and Bush’s plan was insufficient. If Bush is wrong, and the surge is generally regarded as a failure, McCain would have been able to say he wanted more and that would have worked. If on the odd chance Bush were right, he can still claim credit for encouraging a surge.
Endorsing Bush, instead of moving to his right, is either a strategic error, or part of a larger game where McCain hopes to gain something from the endorsement of policy (but what could that be … a Bush endorsement of his campaign does not seem like something of sufficient value to warrant selling out for).
Note: I neither endorse the surge, the war, nor McCain. McCain seems like a nice guy, and he was held prisoner for a number of years, but he is wrong on every issue.