The U.S. hasn't convicted someone of treason for more than half a century. Even John Walker Lindh, who was literally fighting with the enemy against the U.S., was not prosecuted for treason.
Why, so you can stop President Obama being elected for a third term?
To me as an outsider, this is a puzzling part of the US political system. The President has a huge amount of concentrated power within one branch of government, yet approximately half the time, the President of the day is effectively a lame duck with nothing to lose by behaving almost any way they like. Other parts of the government can make that President's job harder, but short of impeachment everyone is basically stuck with whoever it is until their time is up.
I increasingly feel that giving the electorate an absolute power of recall if an elected representative angers enough people during their term would change politics for the better at almost any level. Otherwise, any term of office that is sufficient for reasonable medium- to long-term planning is also sufficient to allow serious damage to be done with relative impunity if the wrong person won the election but the voters only learn that after the fact.
As a side benefit, this also balances the tendency for major elections to be fought on a tiny number of headline issues, with little if any incentive to represent the electorate's interests in all the other significant-but-not-dominant areas, because if you annoy too many small groups of the population, collectively they can become powerful enough to trigger a vote.
I don't think your version of "serious damage" from this issue matches most voters. Even if this were a parliamentary system where sufficient public outcry could force new elections, or a "do over" recall was available (a terrible flaw in the state constitutions where it exists, IMHO), you'd still not be getting the U.S. administration you seem to want. You need to convince the public and then win elections, that's how change happens.
This lack of direct motivation is a systemic weakness in almost any electoral system that involves fixed terms of significant length, and it applies more generally than just the need to choose appropriate subordinates. What you described just happens to be one ineffective case that is relevant to the current discussion.
Look at it this way: how much do you think the average person would pay to get rid of the NSA program?[1] You think it's anywhere near how much money is on the line from Medicare/Social Security/tax policy choices? Or heck, even so-called "wedge issues" like gay rights or abortion rights?
[1] This is, of course, one easy way of valuing the negative utility of any given thing, by asking how much people would pay to avoid it.
Its probably because of the narrow definition of treason written explicitly into the Constitution [1].
[1] http://www.law.cornell.edu/constitution/articleiii#section3