It's actually really hard to tell just how heavily policed the US is. Or, at least to pin down the number of full time sworn in officers (ie, carry badge and gun and can arrest people) that the various federal, state and local law enforcement agencies employ.
For example, DoJ statistics for 2012 have the total full time sworn in LEO population in 2012 at just over 751,000. FBI UCR data for the same year has LEOs at just under 670,000. The US BLS data has sworn LEOs at 823,000.
That's a variation of more than 150,000 officers!
And, none of the above include things like corrections officers, baliffs and jailers, of which there were another 450,000 to 500,000.
And, it also gets even more murky when you look at various federal agencies and how many of their personnel may or may not be recorded in the statistics. If you add all these up, there may be somewhere north of 1 million sworn LEOs in the US.