I haven't followed British politics closely enough recently to be sure, but I'm actually pretty skeptical about the likelihood of the Iraq situation bringing down his government as Charles Dodgson suggests. Tony Blair has been party leader for awhile. Since there is no primary system as such, the candidates are set by the party, which gives the leader some power to stack the deck with loyal soldiers over time.
I actually think Blair might face a different problem - the Queen putting a stop to troop deployment absent UN approval... She is head of the armed forces, after all...
Unlikely, perhaps, but...
UPDATE: Tom Spencer has more bad news for Blair.
