Regardless of whether or not the President of Honduras was engaging in an attempt to subtly overthrow the true concept of democracy in Honduras, and replace it with the barely disguised dictatorship of Venezuela, the method of stopping this transition should not be to engage in a military coup. All that does is sabotage democracy even more substantially, for if the military cannot be trusted to stay out of political squabbles, and will jump in on the side of whomever they support, what trust can the people of the country have that their democratically decided results will be maintained?
Finally, we should be wary of the claims of the elite in government in Honduras. Like many Latin American countries, its government is often controlled by the upper-middle-class, the businesspeople of the nation, and the elite wealthy. They see someone like a Chávez as a real threat, because he finds his power from the poor in society, a group of people who are rarely provided with any true advantages by the governing business owners. Understandably, they fear the reorganization of power that can occur if the underclasses get their hands on the machinery of government. This does not justify their attempts to halt such a reorganization through illegal means.
It has put the United States in a very bad position. If we do not call for the return to power of the elected president, we will appear to be falling back into our meddleing ways that have made us almost uniformly despised in Latin America. On the other hand, if we help reinstate the President, we validate him and his efforts to effectively emasculate democracy in the country, and we will be providing a substantial feather for the cap of Chávez, Morales, the Castros, and their ilk. Nothing like being between a rock and a very, very hard place