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One of my best qualities (in my professional sphere) is the ability to only zoom in on problems, until I get an idea of where to look for them over all in a project. THEN pull back and look at where these types of problems might appear elsewhere in the project. My job isn't to fix them (there are people for that) - I'm hired because I can see the overall scope and areas of risk.
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Let's look at an example, in relation to the Health.gov web site problems, President Obama was (according to his own aids) looking closely at legal implementation details and the problems.
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If you see implementation problems in the details there, this should alert a good Prj Mgr to let someone else handle those details (that is what you pay them for); then pull back your focus and see if implementation details were hampering other aspects of the same project. You would find them in the state reimbursement and a massive problem in your own online presence (i.e. the .gov website).
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Example two, the President's aids say that the President was extremely focussed on the NSA, but as it relates to terrorism and so wasn't informed that we spied on allied heads of state. ... Well, you can't focus on what works (we haven't had an international terrorist attack since blah de blah).. focus on what might become a problem.
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A Prj Mgr shouldn't worry about what is working (again, that is what you pay those guys for), you focus on potential problem areas. We are collecting a ton of data from Americans, right. Is it needed, is it necessary? What else are we collecting and will it bite us in the ass?
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As for Snowden's dribs and drabs of details - that is just sloppy sloppy management. Go through the details that might be released in the future, and do some pro-active risk mitigation! Get ahead of this and see what is going to cause massive problems but provide no profit. YOU, President Obama, should have called foreign heads of state before this was leaked and told them. Let them tell the papers, craft an answer before the Prime Minister of Germany and Spain get their panties in a bunch! Let them tell their press they are on top of it. Right now, you need to find out who didn't give you the heads up on this, and put him a serious time out. If you can't fire his butt, then have hime sort paperclips for a few weeks in a cubby off the mailroom where the workers play horrible rap music 24/7. Maybe he can be in charge of opening mail and looking for anthrax - he'll quit.
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President Bush Two had a different project manager problem. He only focussed on the big picture. He ignored details that might bite the project in the behind for two long. When Chenney or Rumsfeld made huge mistakes repeatedly (Weapons of Mass destruction in Iraq? Greeted with Flowers? Yellowcake in Niger?) stop listening to them!
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And neither man can give an honest, "I'm sorry!" because neither knows what they are doing wrong. Both are working by the same rules that got them there. Well the rules change when you become the USA's Project Manager. Man Up!