NSA has a booth and so does In Q Tel and a few others, but these are very sparsely attended. Where you'll see a line of 200+ for Facebook and maybe 1 person for NSA by accident sort of thing.
A number of the 3 letter agencies have very nice job propositions (you really can do work you can't do anywhere else) but their processes and bureaucracy (not to mention pay etc) really leave quite a bit to be desired.
For example a number of the NSA Presidential Fellows are ridiculously amazing, but for some reason (maybe my lack of exposure) I've not found them to stay in their role, or to necessarily be super positive about it.
Similarly when we were getting offers even with a lot of the red tape out of the way (e.g. already having a high level clearance), it would take months for paperwork - in the meantime you could get a few offers and deadlines for many of the well known companies.
Again similarly there were likely a handful that went to these agencies over the last 6yr and they were never our best + brightest; if you were drawn to that sort of work it made more sense to do a PhD with a NDSEG/NSF fellowship and do an internship at one of the military labs/NSA then to spend years there.
I worked for a well known (in this area) science non-profit agency, and while we did attract good talent, after I moved to the private sector (and literally earning twice the salary) that I found much more brilliant people working at the high paid private sector jobs.
So while I agree that public sector jobs can attract good people, I think that most of the best people are in the private sector where they can earn more money.
I have the opposite perception about this in the US: government jobs seem to be 'butt at desk 9-5' where private sector provides the opportunity for flexibility.
Having worked in public sector (for a small gov't agency in NYC), I know for the fact that most voters or taxpayers don't hear much about most of botched projects or millions of dollars wasted extravagant IT purchases that incompetent gov't career bureacrats make. Or why the last president of my organization was "forced" to resign years ago after a major IT f'up. Normally, there would be no firing, but the scale of the f'up was so gross that the president had to resign, but, despite his public standing as the head of the second largest library system in the country (funded by taxpayers and private donors), nobody got to hear what really happened.
We have some of the best talent in our country. We pay them less, but a lot of people prefer working in the public sector for a variety of reasons. Some are idealists who want to build a better society, others like the flexible hours and the paid sick leave for their children, others again like the relative stability or safety or the fact that they get to work on big projects.
I think the bad image comes from the fact that our scandals are public. When the banking sector does a big project that fails you typically won't hear about it. When the government fails, you'll be reading news articles, blogposts and the likes as well as having researchers from prominent universities trying to pour their take on what the government needs (typically to ask said researchers).
The public sector does fail more though. I think there was a study in the 00's that showed around 75% failures on major IT systems in the private sector and around 85-90% in the public sector. But then we have to digitize an un-digitizable law, so I think this is only natural.
In my municipality we don't do complete failures often, but we don't always succeed in implementing as successful as we wanted, leading to a lack of benefit realization.
That being said, we operate around 370 different systems 50-70 of which we've build ourselves, and most of these are working fine.
I think I'm a nice example. I get headhunter a lot, and I could be making a lot more money in the private sector, but I prefer the public sector because I have Children and since my job comes with paid lunch breaks I work two and a half hours less per week. On top of that, I'm not expected to work 40-50 hours a week despite being in management. I sometimes still do, but then it's typically for interesting projects such as heading the digital voter registration process during elections.
This may be very different in America, but I suspect that the NSA would be able to attract the best of the best on image alone.