I've always thought that this is a good idea. While it makes a lot of sense to have an autonomous entity (government) to distribute resources and production in the public sphere, it seemed to be a stupid idea to have it be responsible for decision making. National Democracy also seems to be ineffective at management when half of the population doesn't agree with the other half, as the OP said.
The major problem of this new system would be economics. Assuming for convenience of argument that we kept the same territorial divide of the current state zones, each state is not economically equal in terms of domestic resources and production. This was the idea of the first confederate states and it was a failure largely because of this very reason. The other problem was that it was governed by an autonomous collective representing states that could never agree on anything.
I think that this could be resolved by keeping the current state territories and giving them autonomous governing, while keeping the federal government intact to perform all of it's administrative duties to preserve the national economy, but stripping it of all legislative power. I think that a federal constitution should still be in place as a guideline, but one that allowed for more state autonomy. It could have such provisions, for instance, as allowing citizens to continue interstate travel for obvious economic and political reasons.
In turn each state would also be stripped of it's confederated power, since there is no need for state senators and congressman without a national collective legislature. The legislature within the state would fall upon either the state government, or any other smaller factions like county, city, etc. whom are better representatives of their constituents.