Facebook (FB) thought it could kill Snapchat. Then it tried.

Snapchat, which lets people send self-deleting photos, videos, and texts to friends, has been enjoying a steady surge in popularity. It’s not hard to see why: Even if you’re not an elected official, the ability to send self-destructing, time-limited messages has an obvious appeal. A year after Snapchat’s September 2011 launch, users were sending 20 million ‘snaps’ each day, and the app ranked just behind YouTube (GOOG) and Instagram on AppData’s list of free photography apps.

In early December, Facebook threw together its own Poke app, which would let users send self-destructing photos, videos, and Facebook messages. It was so closely modeled on Snapchat that it led to speculation that Facebook had tried to buy the smaller company. Facebook put it all together in just 12 days, and TechCrunch’s Josh Constine reports that Mark Zuckerberg wrote parts of the code himself, notwithstanding his minimal involvement with day-to-day programming. The Facebook chief executive officer also lent his voice to Poke’s audio push notifications.

Snapchat users were not impressed. They hated the new app, deriding it as an obvious ripoff. Om Malik wondered why Facebook, with all its engineering and product talent, “can’t really invent any new single online behavior that would keep people addicted to Facebook?” Slate technology writer Farhad Manjoo noted that the attempted Snapchat suckerpunch signaled an innovation deficit at the bigger company. “Facebook shouldn’t be ashamed that it had to copy Poke,” wrote Manjoo. “But it should be ashamed that it never even tried to invent it.”

The attempt to usurp Snapchat’s role only succeeded in boosting attention for the app. According to Topsy, daily mentions of Snapchat on Twitter have jumped from 27,360 to 153,900 in the week since Facebook unveiled Poke:

Topsy Analytics

At Forbes, Anthony Wing Kosner noted a significant uptick in popularity for Snapchat in the past week. (AppData reports that Snapchat is the #4 free app) in the United States:

AppData via Forbes

This isn’t the first time Facebook’s attempts to nudge out competition have backfired. In 2010, geo-location service Foursquare experienced a huge surge in interest after the launch of Facebook Places. Foursquare CEO Dennis Crowley tweeted that it was Foursquare’s biggest day ever, in terms of new user signups. (Consider such moments versions of the Streisand effect for startups: Attempts by larger companies to eliminate or acquire potential threats result in tremendous surges of publicity.)

Still, Snapchat’s future is far from certain. Before the Poke showdown, Eric Eldon reported that Snapchat had raised “north of $10 million” in an investment by Benchmark Capital that valued the app company at around $70 million. Still, plenty of single-serving apps suffer a massive drop-off after a few weeks of hype. (When’s the last time you heard someone talk about Chatroulette?)

For now, though, the Snapchat team must be thrilled with the unexpected attention. On the day of Poke’s launch, co-founder Evan Spiegel released a brief statement: “Welcome, Facebook. Seriously.” A week later, the message seems clear: That which does not kill us only makes us stronger.

Keller is director of social media for Bloomberg News and Bloomberg Businessweek.