From my shopping I find that there are only a few items with clear price increases such as butter and bacon. So I never buy either anymore unless on sale.
If you use the price of gold to gauge inflation then there has been a severe deflation since 1980, oil not that much of a change, silver deflation. Since inflation is a general rise in the price level not just a few products I tend to disbelieve claims of great inflation.
Actually, there are other means of determining the existence of deflation/inflation which would be outside the control of federal authorities. Should there be too great a gap between the claimed CPI and the real one private authorities would quickly be heard. There are even international bodies such as the IMF, World Bank, among others which provide alternative financial data. So there won't likely be too great a divergence.