How to know if my voltage regulator is still working or not
If you connect a normal LED directly to 3.3 volts, it will try to draw a near-infinite amount of current, due to the LEDs I-V curve. This is from a completely random green LED I found:



Follow the horizontal axis to 3.3 volt, and you can see that the current, if possible, would be hundreds of amperes, or more.

This is a pointless exercise, because the LED would burn up in flames before that. Instead, what likely happens here, is that your regulator has a few protections:


  The TPS788xx features internal current limiting and thermal protection. During normal operation, the TPS78833 limits output current to approximately 350 mA. When current limiting engages, the output voltage scales back linearly until the overcurrent condition ends. While current limiting is designed to prevent gross device failure, care should be taken not to exceed the power dissipation ratings of the package. If the temperature of the device
  exceeds approximately 165 °C, thermal-protection circuitry shuts it down. Once the device has cooled down to below approximately 140 °C, regulator operation resumes.


I don't know if it is the current or temperature protection that kicks in here, it depends on the frequency of your "blinking".

If you want to make sure that your regulator is still working, the easiest way is to connect a 22 &ohm; resistor from the output to ground. Make sure it can handle 0.5 watts. Then measure the voltage.