When I'm talking about political institutions, I want to make two sets of distinctions. I see, both from commenters and other conversations, substantial confusion between these two distinctions, so I want to be more explicit about what I'm talking about.
The first distinction, which I'll arbitrarily label "republicanism" vs. "democracy", distinguishes who has day-to-day control over high level public policy decisions. In a republic, the people as a whole choose (or exercise some kind of selective control) those who have institutional authority to make binding public policy decisions on a day-to-day basis. In a democracy, the people themselves, by some sort of institutional means, make day-to-day public policy decisions. (In an authoritarian government, the people exercise no institutional control on the government whatsoever.)
The second distinction is between "pure" and "constitutional" government. In a pure government, the government — i.e. those who make day-to-day public policy decisions — may make any sort of decisions it pleases, and those decisions will be binding. In a constitutional government, there is some sort of well-defined and stable limitation on the kinds of public policy decisions that the government can make and will be binding.
By these distinctions, the present US Government is a constitutional republic. The people as a whole make very few public policy decisions; when they do directly make these decisions, as through ballot initiatives, the process is slow, cumbersome, and infrequent. In contrast, I propose a constitutional democracy: The people themselves take day-to-day responsibility for public policy decisions; and even at the regional and national level, authority is never delegated to individuals. (I'll get into how that works when I describe the People's Government in more detail.) However, I still propose a constitutional democracy: the people will still have limits and constraints on the kinds of decisions they can make binding. My proposal of three more-or-less equal branches of government to provide checks and balances hints, I hope, at the constitutionality of my proposal, but I should of course be explicit.
By placing the implementation of policy in the Civil Service, I implicitly place a constitutional limit on the People's Government: The people may make binding public policy decisions, but it's much more difficult for them to make implementation decisions. The "city government" for example, could not actually issue a building permit: they would have to somehow direct the Civil Service to do so. At the very least, simply making the division into policy and implementation creates a little of a roadblock; I'll talk about additional details that raise additional constitutional roadblocks when I talk about the People's Government and Civil Service in more detail.
By talking about a Judicial branch that closely resembles the US judiciary, I also implicitly bring in a lot of constitutional control. The US judiciary exercises judicial review; the judiciary can directly hold an act of legislation to be unconstitutional and invalid, and refuse to enforce it. For judicial review to be meaningful, there must be explicit constitutional limits on the actions of the People's Government. Second, a judiciary implies a rule of law. Again, I'll talk in more detail later, but the existence of a judiciary, especially a Judiciary of equal standing with the People's Government, entails that the People's Government acts primarily by making general laws rather than arbitrarily deciding cases. (This limitation will apply more to standards of conduct imposed on individuals; the People's Government will have executive authority over the Civil Service and the public ownership and control of capital.)
My fundamental point is not to eliminate constitutional controls on government; I think constitutional government and the independent judiciary are far and away the best innovations of bourgeois capitalism. My fundamental point is to put the people in much more direct control over the institutions of government and the formation of public policy.