I doubt many people hate Button, especially on this forum, though I would say some people are quick with disparaging comments about his driving skills. I think he’s a very strong driver with one notable weakness: tyre warm-up (and perhaps he’s a little more senstive to a bad set-up than his former team mate Hamilton). If in 2013 tyre warm-up is not a problem – as it seems – and the McLaren is good – as it also seems – then Jenson should be a title contender. Note that he did win the title in 2009 even though he suffered from tyre warm-up problems in the second half of the season then, too.
As for my personal preference, my situation is somewhat comparable to @matt90. Prior to 2010, Jenson was always one of the guys I liked to see do well. When he teamed up with Hamilton, this changed for me in the sense that I didn’t like to see him do well at the expense of Lewis. In 2010 there was not much to feel ‘threatened’ about. Jenson finished ahead of Lewis on a number of occasions, but not because he had been faster; cleverer, perhaps, and luckier or less accident-prone. In 2011 that changed, particularly in the second half of the season, when he often better managed his tyres, or even on pure pace on Sunday (as well as not driving into Massa all the time). In 2012 it was Jenson who struggled, but if he takes the 2013 title that will, however petty this may be, leave a sour taste in the mouth with me.
A final thought on his popularity: having the most number of supports does not necessarily equate to being the guy most people root for. Especially because he is such a likeable guy, people might list him as a driver they support, even if he is not their number one favourite. Among the drivers I support are Hulkenberg, Webber, Grosjean, and Ricciardo (I wanted to add Van der Garde recently – in fact, I thought I might like to be the first to support him – but I couldn’t add him yet, @keithcollantine), though only if Hamilton has a bad weekend do I have a sour mood on Monday.