I know I'm very late to this thread
but it's such a great question I'd like to answer it.
Where I am, Lleyton is extremely popular. To give an example, when Lleyton won the US Open, the switch operator sent an email to the entire firm announcing it (it was about 8am here) and despite a strong policy aganst sending non-work related email to all (with 800 people in the office, there has to be!), the response was overwhelmingly favourable. I would guess more people stay up to watch Lleyton's big middle-of-the-night matches than don't. Some people certainly don't agree with particular aspects of his on-court persona, but generally even these people think he's interesting rather than annoying and appreciate his charity work and his commitment to Davis Cup and other Australian players.
However, there are a lot of different kinds of Australian subcultures and I think Lleyton is viewed diffently in them. I work in the corporate world right in the middle of Sydney and virtually all my colleagues and clients are highly educated and relatively successful in their chosen field. Many of my colleagues have worked overseas, quite a few were born overseas and have chosen to become Australians and about 10% are expats here on a medium term basis. Basically, in this corner of Australia:
1. If you asked people to describe Australians, they would be more likely to say "work hard, play hard" than "laid back, with a "she'll be right mate" attitude". This is enforced by the view of overseas colleagues of Australians they have worked with.
2. Xenophobia is frowned on (and in fact very rare) but a decent dose of patriotism is considered healthy.
3. Ambition, hard work and competitiveness are common, respected qualities, though preferably they should be offset by good teamwork and community service.
Remind you of anyone?
Now, many Australians would probably say that inner-Sydney lawyers have nothing to do with the "real" Australia, but in fact over half our population lives in the three biggest cities and we have one of the highest proportions in the world of population working in the commercial sector, so it's a sizeable representation if by no means the only one.
Lleyton has also won many women fans for his public support of Kim and then Bec, and also his defence of Lindsay after Pat Cash's "shotputter" comment. I have noticed this particularly among my mother's friends, for example, who seem to think he's adorable (not so sure this matches Lleyton's view of himself
In fact, I have noticed that many older people seem to like Lleyton better than his age group does. I suspect this is because they don't expect an 18 year old to act mature all the time, and because they know it's unrealistic to expect every player to be Pat Rafter. Or maybe they remember other short, dynamic players and think he could be a whole lot worse
EDIT: BTW, the patriotic aspect is one part but not the only one. Federer is also very popular.