longtimelurker: Our current state of affairs in the UK is very similar (if not more pronounced) in terms of being a one-party state. At the current time Labour hold 408 seats in our parliament out of a total of 659. The next largest party, the Conservatives, by comparison, hold only 163.
Fortunately for us, the current Labour government is really a centre-right government (think Clinton's 'Third Way') rather than extremist. The current situation does allow some necessary evils to be passed through (such as dealing with rising pension costs/NHS reform etc.), however it means that unless there is a MAJOR backbench rebellion (as was almost seen with Iraq), the government just gets it's own way with practically everything and can just ignore protests from everyone else - more like an elected dictatorship. Unfortunately I sincerely doubt this is a situation that will change for us for the next 5 years or so at least - fortunately for you, your houses are a lot more closely fought.