Could an action potential produce few or more neurotransmitters based on the stimulus received?
Short answer  


Widening of the action potential increases neurotransmitter release;
Generally, an action potential results in the release of about one vesicle of  neurotranmitters; 
An action potential does not have to lead to neurotransmitter release - the chance being anywhere between 9 - 100%, depending on the synapse under investigation.




Background

Neurotransmitters are released in packets, called neurotransmitter vesicles: 


Source: Science blogs

Vesicles are released via a mechanism involving Ca2+. When an action potential reaches the synaptic terminal, voltage-gated Ca2+ channels open, which leads to Ca2+ influx. The increased Ca2+ in the terminal leads to release of vesicles.

A study by Sabatini &amp; Regehr (1997) showed that widening of the presynaptic action potential in rat cerebellar cells resulted in enhanced Ca2+ influx, which in turn greatly enhanced neurotranmitter release.  

According to a study in rat hippocampal cells it was shown that, on average, a single action potential releases approximately 0.5% of the vesicle pool from the presynaptic terminal. The presynaptic vesicle pool was estimated to be 100 - 200 vesicles, which hence added up to 0.5 - 1 vesicle released per action potential (Ryan &amp; Smith, 1995). 

An earlier study of Rosenmund et al. (1993) confirms these findings in hippocampal neurons, and investigated the variability between different synapses in greater detail. They found that the chance that a single action potential released neurotranmitters was 9 - 54%. They reasoned that larger synaptic terminals, or terminals triggered by long-term potentiation have a higher chance of releasing neurotransmitter. Moreover, such terminals with enhanced release probability may also have a higher chance of releasing multiple vesicles per action potential. They predicted that 54% of release events from such enhanced terminals may release multiple vesicles per action potentials, whereas just 9% of normal terminals may do this.


References
 - Rosenmund et al. Science 1993; 262: 754-6
 - Ryan &amp; Smith, Neuron 1995; 14: 983-9
 - Sabatini &amp; Regehr, J Neurosci 1997; 17: 3425-35