The question is, during the seven days of celebration after a wedding, is it an obligation to make a Minyan (quorum) of at least ten men in order to be able to recite the 7 blessings during the meals that week? Or does one only do the 7 blessings if a Minyan happens to be present?
We are told in the Gemara of Kethubboth that at a meal after a wedding there was no Minyan present and Rab Ashi recited only the last blessing. From this we learn that it is not an obligation to assemble 10 men for this purpose. Indeed, this is the custom, that we recite only the 7th blessing in the absence of a Minyan.
So, other than the 7 blessings of the Nisuin under the Huppah which does require 10 men, if there is a reason why it is difficult to invite a Minyan, or too expensive for the family, then it is not required for the meals during the week after the wedding. However, if one is able to, and makes the effort to have a Minyan for the meals, it is considered praiseworthy.
(See Rab Pe'alim, Heleq Dahl, 'Eben Ha'Ezer, Waw)
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