The U.S. Postal Service is a bastard child, a federal agency spun into a quasi-private concern under the direction of commissioners appointed by the president, with the consent of the Senate. That should be enough to explain why it never seems to keep its head above water, financially. The latest plan to close 677 branches is just the latest example of how poorly economics and politics mix.
According to the Washington Post, In late August the USPS removed more than 200 sites from the kill list, 30% of the total. The 677 had already been a considerable reduction over the 1,000 the post office had first warned the Postal Regulatory Commission it might have to shutter. These 200 represent one-half of 1% of all Postal Service facilities. To many Americans, closing a town's post office is tantamount to declaring it inconsequential. Given the political nature of the USPS administration, expect representatives and senators to react with NIMBY* vehemence to any plan that disrespects a town in their district. This makes saving any money by closing a branch a dicey proposition.
These closings represent a only a penny stamp's worth of savings in the massive USPS shortfall, thanks to the recession. Among more substantive steps being considered is dropping one day of delivery per week. Some branches have taken other, more mundane steps to reduce expenditures. For example, some offices in Columbus, Ohio, have started to close for an hour for lunch, taking many locals by surprise (and upsetting more than a few).
Given the political nature of the beast, I don't have much confidence that much cost-cutting will be permitted. If I were you, I'd be investing in Forever Stamps, because rates are probably on their way up significantly.
*NIMBY: Not In My Back Yard