In August 2012, the Anchorman quote, "That escalated quickly," became tremendously popular almost overnight. Which is to say, it escalated quickly.
Historian Vanessa Heggie spotted the sharp spike of interest in "Well, that escalated quickly" on Google Trends, then shared her findings with a tweet that's been retweeted over 2,220 times in the past 24 hours. Yes, it's escalated quickly, too.
This... this is a joke by google, right? pic.twitter.com/lT51sHn23G
— Vanessa H (@HPS_Vanessa) April 19, 2016
But why did this quote spike in the summer of 2012? Anchorman was released in 2004, and its sequel, Anchorman 2: The Legend Continues, wasn't in theaters until 2013. Know Your Meme, the closest the internet has to an encyclopedia of internet memes, says the earliest popular usage outside of the Will Ferrell comedy came in a 2007 webcomic from I Heart Eddit. In April 2011, YouTube user Niamh Joyce posted an excerpt from the film that begins with the actual phrasing of the line, "Boy, that escalated quickly." The video currently has 1.45 million views. The video is five years old, but its earliest comments date back to four years ago, which would place its viral success somewhere in 2012, alongside the trend in popularity of the quote.
Also in 2012, around the time of the success of Niamh Joyce's video, Know Your Meme reports that an image macro of the phrase, "Well, That Escalated Quickly," along with a screen-capture from Anchorman, began to appear regularly on forums and blogs like Reddit and Tumblr.
An example:

It's fascinating to compare the interest in "Well, that escalated quickly" with other popular quotes from Anchorman. Below, we have "That escalated quickly," which is generic enough to be used in a variety of situations, paired with "I love lamp," which is non-sensical and specific to the film from which it came.

The takeaway seems to be, off this comically limited data, that a movie in-joke, has a moderate but lasting popularity. But a broader line can gain traction in popular usage by a larger audience.
So we test that theory, and compare both lines with three more popular lines from the film, one specific and two broad. Blue is "That escalated quickly;" red is "I love lamp;" yellow is "I'm in a glass case of emotion;" green is "Don't act like you're not impressed;" and purple is "I immediately regret this decision."

The other lines barely bump on the graph.
Okay, so we try popular lines from other films. Blue is "That escalated quickly;" red is "You talking to me;" green is "Frankly, my dear, I don't give a damn;" yellow is "I am your father;" and purple is "May the force be with you."

The consistent flatness of the older quotes — "You talkin' to me" and "Frankly, my dear, I don't give a damn" — appear to represent a general cultural awareness of the quotes, similar to "I love lamp." While the annual spikes of interest in "May the force be with you" align with the Star Wars fan holiday, May the 4th. If flat tells us the awareness of a quote, spikes represent usage.
The rapid spike and gradual decline of "Well, that escalated quickly" then doesn't seem to reflect interest or awareness of Anchorman or the quote's context within it, but the popularity of the phrase as an unintended and standalone meme byproduct.
The movie and its quote are now all but divorced from one another, which brings us to this one last graph:

The popularity of Anchorman and "That escalated quickly" have no clear correlation. All of which is to say the popularity of "That escalated quickly" actually escalated quickly not because of its film's success or popularity, but because the internet made the quote its own.