BEYOND THE CULT: The National are ready for their close-up.

“We’re going to become one of those bands that you just want to play one song,” commented the National’s guitarist Bryce Dessner from the stage at the second of two sold-out shows the Ohio-bred, now Brooklyn-based fivesome played on successive days downstairs at the Middle East. He was reacting, with mock concern, to all the fans shouting out requests for “Abel,” a moody, literate, poetic track from the band’s 2005 album Alligator (Beggars Banquet) that became a college-radio hit and created the big buzz for their new Boxer (also Beggars). The irony was palpable: if there’s one mold the National don’t fit, it’s that of the one-hit wonder. As they’ve proved going all the way back to their 2001 Americana-tinged homonymous debut on Brassland and forward to the more orchestral Boxer, they’re all about well-crafted songs delivered without a wasted note by the brother teams of Bryce and bassist Aaron Dessner and guitarist Scott and drummer Bryan Devendorf, along with singer Matt Berninger. The National have mostly flown just beneath the commercial radar, pleasing a small but dedicated cult audience at venues half the size of the rooms they’re playing on their current sold-out tour. Alligator changed all of that, as fans began to pour out of the woodwork in the months leading up to Boxer, which was leaked well before its actual release.

But the band hardly seemed aware that anything was different as they took the stage Thursday evening, wide-eyed and scruffy-faced, with modest confidence. There were a few slow, uncertain points in Thursday’s show, but by Friday evening they’d worked out any kinks. The blond, lanky Berninger cocked his head slightly, gripped the microphone with both hands, and squeezed his eyes closed to sing. His easygoing elegance and signature baritone can you forget he’s singing anything but your typical love song — Alligator’s “Karen,” for example, has him masturbating to images of ballerinas and asking his girlfriend to “fuck me and make me a drink.” Boxer’s bluesy “Racing like a Pro” — which at the Middle East was capped by a dynamic violin solo— showed off the band’s increasing musical range. And in “Mr. November,” Berninger, eyes still closed, let the music overtake him as he led the audience in frenzied shouts of “I won’t fuck us over.” Nobody was crying out for “Abel” after that.