How much advance notice does the FAA have to give for a TFR?
The FAA can issue TFR's on short notice, and if you are flying a slow plane or a fast plane far they may very well pop up while you are inflight. While things that cause TFR are often planned in advance like the super bowl there are plenty of last minute things like a wildfire or a quick movement of the President that will force a fast TFR to "pop up". Even the FAA admits they can can be unexpected 


  TFRs can pop up unexpectedly, so before any flight, be sure to
  research NOTAMs, check the TFR list online at http://tfr.faa.gov, and
  call Flight Services for updates at 1-800-992-7433.


I can not find any regulations sating the FAA has a minimum amount of notice time they must give. 

A pilot flying VFR in an airplane not radio equipped is always at risk of busting one of these. But if you are in a radio equipped aircraft taking flight following or monitoring your local FSS is a good way to be aware of these kinds of events. 

This AC covering TFR's does not list a minimum amount of time they must be filed before becoming active.