The upstairs/dowstairs/backstairs of White House?

I'm making a guess here, so you may want to view more opinions.

I think it refers to the public profle of the people refered to. those upstairs are likely to have a high public profile and are seen going about there task. It may be that they staff who are currently more in favour with the president.

Those downstairs are behind the scenes and make things work kinda the engine room of the whitehouse but have a low public profile. they are currently less in favour with the president.

The back stairs staff may be seen as the maintenance workers. doing their job quietly behind the scenes, fixing mistakes and smoothing over rough patches. As the article mentions they tell the press who is currently in favour with the president.

I think that DP has got this right. This is the second quote you've provided from Mr. Reston, and my opinion of his writing is declining. He is using figures of speech (perhaps thinking it improves his style) to make his points, but i think he is using them ambiguously. There was a television series made in England which was popular in the United States at about the time of the Reagan administration which was entitled Upstairs-Downstairs. Upstairs refers to an aristocratic family, and downstairs refers to their servants. Backstairs has a figurative meaning in English, usually but not always referring to politics, and means those things which get accomplished away from the public eye. In England in the centuries when aristocratic or wealthy men and women employed servants and lived in great style, tradesmen and people soliticing were not allowed to come to the front door of the house. If they attempted to do so, they would be sent around to the back of the house by the butler or maid who answered the door. So a figurative expression arose about doing something by the backstairs, that is, doing something which is not in the public eye.

Mr. Reston seems to have read too much of the "Toward more colorful speech" section of the Reader's Digest.

Twice in one day You've agreed with me Setanta. That must be something of a record.

BTW I apologise for the spelling error. I know better than that.
those upstairs are likely to have a high public profile and are seen going about there task.
Should read "their tasks".

In addition I need to clarrify that those referred to as "working upstairs" do not necessarily actually have their offices upstairs in the White house. They may in fact be employed in a completely different building. The figure of speech referes to their status within the whitehouse heirarchy

A good point. In fact, there are offices in the Executive Office Building just across the street.