Our government does function today according to these principles. In fact, there are times when these principles seem to undermine the government’s ability to act.
In our system, the Congress and the President have to agree in order for a bill to pass (unless Congress can override a veto). We have often, in recent history, been in situations where one or more houses of Congress was controlled by the party that did not control the presidency. This has led to a situation where very little can be done because the two parties cannot agree on anything.
This sort of conflict (which can be seen, for example, in the “fiscal cliff” that we are facing in December) shows that our government is still clearly functioning by these principles.