You can't apply for British Citizenship until you've been in the UK for at least 3 years. If your wife is eligible she could try applying though you may not have enough time to get a passport before Christmas
My wife applied for a tourist visa at the US embassy in London last October (just after she got ILR). It was a reasonable painless process - she spent a few hours at the embassy and they sent her passport back with a 10 year tourist visa a day or so later.
