You're suggesting the half that wants smaller government impedes the day-to-day productivity of the half that wants it bigger?
Some things work well in government given limited resources. Other parts of government seek bigger and bigger budgets to implement ideological goals, no matter their efficiency.
(Any amount of money spent is justified by the end goal since the purpose of government is to print however much money is required to ensure complete social welfare.)
The half that wants it smaller, when it succeeds, guts the government, with the result being that whatever remains is incapable of properly carrying out the duties it is still assigned.