I don't think I ever made an opening week prediction, so I have no words to swallow.

(Maybe I did and I don't remember, though.)
Call me crazy, but I'm sort of to the point where I don't believe promotion plays that much of a role in determining the success of an album/single. Very few promotional stops actually attract significant attention or generate much public interest. The most memorable and talked about performances occur during highly publicized events like the Grammys or the VMAs. A stop at GMA or Kimmel creates a small (and very short lived) blip on the radar, and generally these performances/interviews don't even resonate strongly with anyone but the dedicated fans who go out of their way to tune in. So great, Britney drops by Jimmy's show and does a little skit and gives a performance that pleases the fans and is viewed by the million or so (that might be an overestimation) people who bother to watch Jimmy on a regular basis or tune in by accident. It's not a major event in the minds of the media or the general public, and even if she has been making more public appearances than she did with the last album there isn't enough attention being generated by these appearances alone to generate another 500,000+ opening week. Ask 15 non-music-obsessed folk to name Britney's two latest singles. (Use the word "hit". I find anyone who doesn't follow the music industry is confused by the term "single".) You might get 5 people who could name both songs. Ask the same 15 people if they watched her on GMA or if they even knew she would be on there. At the very most 3 out of those 15 people will say they knew about her appearance, and out of those 3 only one bothered to watch (and that was probably because they just happened to have the TV on the right channel at the right time). I say that as if it's something I've really researched, and I haven't, but I'm relatively certain that if I were to conduct such a survey my results would be eerily similar to my estimation.
So what did Britney have working in her favor that helped make
Circus such a smash success during its opening week? She had an established presence with the media and a discernible connection with the public. In the grand scheme of things I don't believe that her promotional appearances last era had as much of an effect in determining her opening numbers.
Circus was Britney's triumph story, her return to form. Britney was a cause that both general public and the media could get behind. She was someone to rally for and she kept us on the edges of our seats. Britney might not have been making public statements, but we felt a real connection to her because she had been (arguably) the most important cultural figure in the world (for mostly the wrong reasons) for several years leading up to the release of
Circus. Britney's prominence in the lead-up to the release of
Circus was just insane. And that's really the last time she had a prominent presence with the media or the general public.
Circus was released, she looked good, everyone was happy, and she went into hiding. What sort of updates did we have on Britney's life from early 2009 to late 2010? Very few. People have a genuine curiosity when it comes to Britney. It's her prerogative to keep a low profile, and after everything she's been through, who are we to fault her for being wary of the public eye? People are intrigued by her, she's the only real icon to emerge from her group of pop music peers and people want to have a connection with her, though. Britney can survive simply because she's an icon and there's always a decent level of excitement generated by anything she does. Those two things are enough to earn her 300k debuts for the rest of career. The most successful artists of the moment also lead intriguing lives, but what separates someone like Lady Gaga from Britney Spears in 2011 is that Lady Gaga is deeply invested in her public persona and does not shy away from the spotlight. Before she was jaded by fame Britney knew exactly what to do to keep the public and press tantalized, and I think if she regains that magical spark that made her such a lovable figure she can potentially have another
Circus-esque debut.
Now to answer a question that will immediately be posed by the girls in this thread with questionable intentions:
But if all she needs is a little attention from the press to be successful, why isn't Blackout her best selling album?
The sort of attention she received during that era isn't the sort of attention that's conducive to launching successful albums. Who's going to buy an album from someone who, at that time, was the go-to out-of-control celeb and viewed by most as a total ****-up? Only the most dedicated fans showed up to support her.
These promotional efforts seem like a big deal to all of us, but I think it's important to remember that ATRL is a very singularly focused community. In our eyes, any performance by any random pop star is worthy of 20 pages of discussion, but people who are not music/culture obsessed are not on our wavelength. Generally speaking, an average Joe/Joanne sees a performance by Britney or anyone else on a late night talkshow or an early morning news program and they're content to forget all about it and move on with their day. At ATRL we can't help but dissect every note and move until it's no longer enjoyable to watch said performance. We're so dedicated to our favorite pop stars that it's a major event when, for example (this never happened), Ke$ha gives an interview saying she likes the smell of her own farts. Each interview and performance excites us to no end and because of this we expect the tiniest bit of promo to do wonders for an album or single. These performances and interviews do have some effect, but I can't help but feel like they're not nearly as important in determining the success of a project as we'd like to think. I'm convinced that the quality/catchiness of the music, the sort of relationship the artist has with the public and the media presence of the artist are the most crucial factors in determining how well an album sells; a million live performances can't compare to those things. Katy and Christina have made a million high profile promotional appearances. Were their album sales not lukewarm? Katy has the benefit of having catchy music, thus she can have successful singles, but neither of these girls have a very interesting public profile and the general public is not captivated by most of the happenings in their life.