Did you watch Tuesday night's presidential debate on one screen or two? If you answered "Why the heck would I need two screens to watch TV?," then you missed half the show. The rest of it was on Twitter, where the nation's journalists, comedians, politicians and armchair pundits were busy dissecting, fact-checking, spinning and riffing on every word the candidates uttered, almost as fast as they could utter it. If you haven't experienced this for yourself, you're probably tempted to dismiss it as noise. And perhaps it would be, if it weren't so influential.

If you've watched or read a news report about the debates this week, chances are it was shaped in some way by Tuesday night's sprawling, real-time, Twitter-hosted conversation. For those tuning in without a second screen, Mitt Romney's awkward remarks about trying to find qualified female applicants for Massachusetts cabinet jobs might have induced a quick cringe. But if you were simultaneously logged into Twitter on your laptop or smartphone, you knew within moments that the phrase "binders full of women" was going to haunt him. "Romney's binders" parody accounts popped up and attracted thousands of followers, a "Binders Full of Women" Tumblr page made the rounds, and the hashtag #bindersfullofwomen rocketed to the top of the site's trending topics list. Users who clicked on it were greeted with a promoted tweet from the Obama campaign urging them to donate, as the campaign rushed to capitalize on the meme.

Within hours Romney's "women problem" had resurfaced as a campaign issue, with the Boston Phoenix fact-checking his claims about hiring women and The New York Times weighing in on how they could swing the election.

Granted, all of this appeals mainly to the subset of the population that truly cares about politics. That's part of why Twitter, for all its notoriety, is used regularly by just 16 percent of the U.S. adult population, according to a recent Pew study. That modest figure belies the media's frequent comparisons of Twitter to Facebook, which counts half of all American adults as active members. You can debate Facebook's pros and cons, but its fundamental value proposition is universal: It promises to keep you connected to your friends and family.

Twitter, in contrast, remains a niche service. It borders on an obsession for many media and PR types, celebrities and athletes, comedians and wonks, who want to broadcast their ideas to a wider audience. But the average working person would rather relax in front of the TV with a beer most nights than engage in an online battle of wits and one-liners.

Twitter knows that, and it has a plan. Rather than encouraging more people to embrace the service as an active medium, the company wants to push the site as a passive experience. Twitter started as a social network, then became a real-time news feed and sounding board for public figures. Its new goal is to become everyone's default second screen for everything, from presidential debates to the Arab Spring revolutions to the NFL. In short, it wants to be a chatty, illuminating, digital companion to all of the news and entertainment you consume. And it has been tweaking its site in recent months to make sure that you never have to tweet anything yourself, or even sign up for Twitter, to take part.

When I was first planning to write this story, I thought I would have to make the case myself that this represented the company's surest path to mainstream-media status (and a blockbuster IPO). But lo and behold, Twitter CEO Dick Costolo made it himself on Friday. In a radio interview with Marketplace's Jeremy Hobson, Costolo laid out his vision of Twitter's niche:

Costolo: I think the role that it's playing in society right now is that we used to have a filtered, one-way view of events in the world from the media — whether it was a sporting event like the Olympics or an event like the presidential debates last week. . . . Now, with Twitter, people want to know what everyone else thinks and we're getting this inside-out, multi-perspective view of what's going on right now as it happens from everybody else that's watching the same thing we're watching. . . .

Hobson: So you see it primarily then as a media entity, as something that would compete with the other news outlets that we have?

Costolo: No, I view it as very, very complementary to the news outlets.

Twitter is far from the only company thinking along these lines. "Social TV" is one of the hottest new tech categories, with startups like GetGlue and Zeebox and established companies like Microsoft (through its Xbox Live service) all trying to persuade the public to log on, check in and ultimately buy stuff while they're watching the boob tube.

But Twitter has a big edge over these upstarts, because it's already populated with most of the famous people in America, who are generating and sharing more worthwhile content every minute than any human could possibly process. Of course, it generates more than its share of worthless content as well. And during an event like the first presidential debate, which generated an estimated record 10.3 million tweets, it can get so raucous and cluttered as to become nearly intolerable. But Twitter is working on that.

One of the first examples of Twitter's latest pivot came in June, in the form of a partnership with NASCAR that flew under the radar of the coastal media. When it was smaller, Twitter relied on hashtags to organize tweets around a topic or event. These days, clicking on #nascar on race day brings an overwhelming torrent of 140-character bursts, many of which are redundant, obnoxious or otherwise unenlightening.

Now, there's a special landing page for NASCAR fans, twitter.com/#nascar, that features a carefully curated list of drivers, announcers, commentators and influential fans. That way, new tweets appear in the feed at a manageable pace, and you can peruse them without feeling like you're in a NASCAR race yourself. Twitter has since repeated the NASCAR experiment on a larger scale with a succession of other televised events, from the Olympics to the presidential debates.

Unlike Twitter's homepage, you can access these event pages without logging in to the service. That's important, because Twitter has always struggled with its barriers to entry: You have to sign up, figure out whom to follow, figure out what the heck they're talking about once you follow them, and then figure out whether you have anything to add to the discussion — knowing all the while that whatever you say could be held against you by your friends, your employer or BuzzFeed. These were the site's biggest obstacles to mainstream popularity way back in 2009, when Slate tech writer Farhad Manjoo wrote that the average Internet user shouldn't feel compelled to join the then 2 1/2-year-old service. They remain its biggest obstacles today.

Even if Twitter realizes its wildest second-screen dreams, it will probably never have as many users as Facebook. For all its virtues, double-screening can be cumbersome and distracting, and if there is actually someone else present with you as you're watching, you'll be hard-pressed to even acknowledge them, let alone enjoy their company.

Yet second screens may only be an intermediate step. If Twitter succeeds in integrating itself thoroughly into the viewing experience, the site could eventually end up converging with TV itself, so that you both watch and tweet on the same interactive screen. Then we'll all be Twitter users, whether we want to be or not.