Are jet engines affected by small bird (e.g. hummingbird) strikes?
All turbine engines must pass a series of tests, including water ingestion (flying through clouds) and bird strikes. For bird strikes, the following article does a good job explaining the requirements to pass bird strike testing:
Aircraft Certification for Bird Strike Risk

It cites 14 CFR Part 33-77 'Foreign object ingestion - ice' (although 14 CFR Part 33-76 'Bird ingestion' seems more appropriate) and EASA Airworthiness Code CS-E 800 'Bird Strike and Ingestion' as sources.

14 CFR Part 33-76:


  (4) A small bird ingestion test is not required if the prescribed number of medium birds pass into the engine rotor blades during the medium bird test. 
  
  (5) Small bird ingestion tests shall be conducted so as to simulate a flock encounter using one 85 gram (0.187 lb.) bird for each 0.032 square-meter (49.6 square-inches) of inlet area, or fraction thereof, up to a maximum of 16 birds. The birds will be aimed so as to account for any critical exposed locations on the first stage rotor blades, with any remaining birds evenly distributed over the engine face area. 
  
  (6) Ingestion of small and medium birds tested under the conditions prescribed in this paragraph may not cause any of the following: 
  
  
  More than a sustained 25-percent power or thrust loss; 
  
  
  The engine to be shut down during the required run-on demonstration prescribed in paragraphs (c)(7) or (c)(8) of this section; 
  The conditions defined in paragraph (b)(3) of this section. 
  Unacceptable deterioration of engine handling characteristics
  
  


EASA Airworthiness Code CS-E 800


  (d) Medium and small birds ingestion tests. Engine ingestion tests and analysis with medium and small sized birds must be carried out as specified below. Alternative evidence may be acceptable as provided under CS-E 800 (f)(1). The small birds test will not be required if the prescribed number of medium birds pass into the Engine rotor blades during the medium bird test. 
  
  (B) Small birds. One 85 g bird for each 0·032 m2 of the inlet throat area or fraction thereof with a maximum of 16 birds, distributed to take account of any critical exposed 


For more information, refer to 14 CFR Part 33-76, and EASA Airworthiness code CS-E 800.

One more thing to add - the documents do not include any tests for single small birds, only flocking small birds, and use birds that weigh 85 grams. Humming birds do not flock, and 85g is more than most humming birds weigh. That being said, the tests do include much larger birds, and all commercial jet engines found on commercial airlines certify large bird strikes, so it's likely that tests with small bird strikes are not conducted. Bouncing off of physics - if a turbine can withstand a large bird strike, it won't even feel a humming bird strike, therefore it is not a required test if the engine already certified with large bird strikes.