I agree that the administration does not do their homework very well -- in some cases, such as defending freedom of religion or free trade, they failed miserably. But I am afraid that I can not really comprehend what a "maximum winning coalition" substantially means, as opposed to a more plausible, at least to me, and more established theory of "minimum winning coalition" (see Riker, 1962, for example).
A "maximum winning coalition" assumes that the winner is somewhat irrational by not picking a low-hanging fruit of smaller coalition for better delivery -- and bigger rent to redistribute within the coalition.
In economic jargon, it is like that he left a 100 dollar bill he saw on the street when actually nobody can prevent him to pick it.
Now, when you see someone did it, you can think that either he's irrational (or maybe foolish); or, he is just rational but it costs him a lot, albeit not directly observable, to grab the money.
The proponent of "maximum winning coalition" argument seems to believe in the first possibility. I am, however, for the argument that the current administration, a large coalition, is still a "minimum winning coalition", given big transaction cost faced by the winner should he exclude the current elements of the administration.
Such cost is stemmed from the effective ability of the (election) losers to hijack the administration policy and rents redistribution -- especially in our existing murky business of political campaign finance transactions, where, it seems to me from series of KPK saga, everybody get the money from everybody.