And it seems fairly clear that he did, for most Americans. But I disagree about seeing them as the only people he was supposed to be talking to. He'd got them on side already, without opening his mouth. The terrorists had done that already.
One think worth noting about Blair's speech - at no stage did he feel it necessary to refer to what is happening as "a war". That was no accident, and in my views it's a pity others didn't do the same. Avoiding the word in no way softens the action, but using it certainly doesn't help keep heads clear.