Andrew B, you're right in implying that a tune cannot be cheap, it'$ all about the money.
In terms of its quality, certainly, a tune can be cheap. Defining a "cheap" tune however, is a difficult task, because "cheap" does not necessarily imply "bad". A bad tune is obviously one lacking in invention, interest, direction, range, cohesiveness and perhaps going a step further one that is underpinned by uninteresting harmonies.
By contrast, a cheap tune may have some or all of the elements of a good melody present, but perhaps in the wrong proportions, or perhaps used in a way that is formulaic and derivative. To support that type of definition on an exam paper, one would obviously have to offer a bevy of examples... and my school days are over. I suppose then the ultimate reference for a non-exam-writing pundit is intuition... One simply knows a cheap tune (Nessun dorma) from a good one (2nd mvmt of Sibelius' 3rd).