Consensus is not only possible in government is essential and used today. When we vote we take the candidate who gets the largest vote. When congress passes a law they need a specific consensus to pass the law. We may never have everyone agreeing on something but a general consensus is still used.
Consensus governments are possible, it just takes certain unifying factors that everyone can agree upon. If fixing the economy is the major factor, then a consensus can be formed if many politicians agree on how to fix the economic maladies occurring in one particular area. The problem is that with more people on the planet, there are more differing opinions as to how to solve the problems of the world.
Yes, consensus in government is possible, because governments operate by consensus in some circumstances. The European Union operates largely by consensus, and they have come to many agreements that have made Europe stronger. The United Nations is another example. With consensus, if no one can agree than nothing gets done. There is a strong incentive for government representatives to work together.
No, consensus in government is not possible. There are too many politicians vying for power in governmental structures. In addition, these politicians represent too many political parties. The conflicting ideas of these politicians and political parties cause the lack of consensus as is. Thus, it is not possible for consensus to be reached.
I do not believe consensus in government is possible. In fact, I don't even think that's the point. The government is suppose to be there for the people to seek out and enact laws for the people. There are obviously a plethora of topics that don't have a clear answer and the government is in place to make final decisions on these topics, which require people who support both sides.