You absolutely can get penalized for building links too quickly if those are not natural links.
Google has been around long enough to know the difference (in most cases) between natural link growth and someone trying to fake it.
If you think that they cannot tell when someone is spamming with social bookmarks or spamming with mass spun article submissions then you are fooling yourself. Engaging in those activities will raise a flag especially on new sites.
I see the argument all the time where people say "If you could get a site penalized then all we would have to do is spam our competitors and we would move up in the rankings."
I can tell you from firsthand experience that you can in fact spam a site and send it to the abyss. So can countless other people who have experienced what is often referred to as the Google sandbox.
If you have a site that is less than a couple years old you most certainly can get it penalized (quite easily actually if you are good at spamming) and sent down 1000 places in the search results.
It is harder to do to an older site that has a clean history. Every brand new site is on probation with Google until Google learns your behavior. Over time if you behave yourself you begin to develop trust. Then when someone else tries to spam you, Google looks the other way. But, when a site is new, they will most certainly penalize it.
But what about viral activity?
Google can tell the difference between something that goes viral and something that people are faking interest in. They can tell because viral activity on one website will bleed over into other similar viral characteristics in others.
For instance, if something gets a lot of votes on Digg, it will also get a lot of links from blogs, links from Facebook, Tweets, Stumbles and Reddits. You will probably also see a corresponding rise in the number of people searching on Google for that related keyword. That is what real popularity looks like.
When something truly goes viral, Google does not penalize it because they can tell from all of the signals that the interest in that content is real.
Someone who is faking it will have hundreds or thousands of links appear from one or two kinds of places without the corresponding follow through from other places.
Long story short -
1) Yes you can build links too fast if you are using spam - try it - If your website is new, you'll find out.
2) It is very hard to fake genuine viral activity