The Census Bureau has made their data available for download for a looong time, both over the Web (including a bunch of different interfaces for slicing out just the data you want -- see http://www.census.gov/main/www/access.html) and FTP (http://www2.census.gov/) All the stuff that's available via the Web service is already available via download, along with a lot more. They don't provide it in SQLite format AFAIK, but they do offer a range of other formats that should be easy to get into SQLite if you wish.

If there's any problem with their downloadable data offerings, it's that they have so many of them that it can be difficult to figure out exactly which one has the data you're looking for.