Does the Low State in NE555 go to GND?
With that particular circuit yes the output should go close to ground.

If it is not, either 


the 555 is sick or  
you MUST be pulling current from somewhere else... or  
perhaps the oscillator is still oscillating at some higher frequency, or,  
Your 5V supply is not flat DC.


Using a scope would help a lot.

You could try lifting the output pin and see if it still does it and measure what the voltage is at the top of the LED to eliminate item 2.