Is reduction potential and stability related? Suppose the half reactions:   

$$\begin{split}\ce{Na^+    +  e^-   &amp;-&gt;  Na} ~~~~~~~~~~~~&amp;\text{ $E^o = -2.71$}\\
\ce{Cu^{2+} + 2 e^-  &amp;-&gt;  Cu} &amp;\text{ $E^o = +0.34$}\end{split}$$

Can I say that $\ce{Na+}$ is more stable than $\ce{Na}$, so $\ce{Na+}$ has negative potential to reduce? If so then can I also say that $\ce{Cu^2+}$ is less stable than $\ce{Cu}$ so $\ce{Cu^2+}$ has a positive potential to reduce?
Remember that reduction potentials do not have any meaning by themselves. They are measured against a hydrogen cell to which arbitrarily we assign the value $E^0=0$. You can compare between different potentials. For example, in your case, you could say that that $Cu^{2+}$ has a greater tendency to be reduced than $Na^+$  because its reduction potential is more positive. However, I do not think the potential itself tells you anything with regard to the stability (and, in any case, what do you mean by that) of the species involved in a particular half reaction.