I seem to remember a day when Bush and Blair had a joint news conference and Bush seemed particularly peeved that day. Peeved at Blair in fact - it was the day they were running late for a conference... who knows but it sure wouldn't surprise me if Bush gave Tony a dressing down over that. Do you remember when Rummy candidly said something to the effect that we would go to war with or without Britain? The British press absolutely hyperventilated over that comment. Rummy later suggested that his comments were blown out of proportion. Perhaps Rummy's comment was a very public statement to Blair: we can live without you.
I do remember that.
Clinton was probably trying to talk Blair out of it.