What is the most important determinant of a household's consumption spending?

While this is not a hard and fast rule, the most important
determinant of a household's consumption spending (in absolute terms) is their income. 
A household generally spends more as it makes more in
income.

This is, of course, not always true.  There are a
number of variables that can intervene and throw this relationship off.  For example,
the number of people in a family and their ages will have a significant impact on the
number of dollars that the family spends on consumption.  So will (in a less easily
measured way) the family's values -- are they thrifty or
not.

But the general rule is more income = more
consumption.