The difference is about generic specification. When you say "No tenemos fecha" fecha is undefined; there are many dates available. But, saying "No tenemos una fecha, the date is no longer generic and is countable. The real intention is to emphasize the fact that there is no date available (of course, we are not really talking about a specific date.) Is the same as saying We don't have **even a single date available**.
Here are several ways you can emphasize:
No tenemos fecha (no emphasis)
No tenemos una fecha (strong emphasis)
Also remember that in Spanish double negation is still a negation.
No tenemos ni una fecha (strong emphasis)
No tenemos ninguna fecha (mild emphasis)
Other examples are
No tenemos naranjas (We are talking about naranjas in a generic sense)
No tenemos una naranja (Although not a specific orange we are emphasizing strongly that we don't even have one)
No tenemos ni una naranja (We are also emphasizing that we don't even have one orange.)
No tenemos ninguna naranja (The most natural way to say it in Spanish; with a mild emphasis.)