Just ask the Clash. It’s a lot of pressure being the Only Band That Matters. For those punk pioneers, the strain proved too much. But Wilco—one the most critically gushed-over groups of the past decade—is handling its responsibilities with surpassing grace.

After surviving the expulsion of long-time co-leader Jay Bennett (who was in a legal struggle with Wilco when he overdosed on painkillers in 2009), Jeff Tweedy’s Chicago-based outfit flourished this decade with a new, improved front line focusing on the tasty peregrinations of guitar wiz Nels Cline. After a three-punch knockout delivered by the sequential releases of Yankee Hotel Foxtrot, A Ghost Is Born, and Sky Blue Sky, as well as a killer live CD called Kicking Television, it shouldn’t shock that 2009’s Wilco triggered the least wildly enthusiastic response of the band’s 16-year career.

“With every new record,” says bassist John Stirratt, calling from Wilco Central in Chicago, “the blogosphere is more in your face with its opinions. We used to have to wait for reviews. But I think we learned early on that disappointing some fans is part of the process. You just hope that you pull more people on than you lose each time.”

He’s in an excellent position to know. Besides the recently cleaned-up leader, he’s the only remnant of the founding lineup, and he thumped alongside Tweedy in the pioneering Uncle Tupelo.

“We went through this, in small ways, over the years, with Tupelo and the first few Wilco albums. It taught us a pretty good lesson that, at the end of the day, you simply have to make music that you enjoy, and that others will come along for the ride if you are lucky.

“I think now people are looking to us for a real stance on every record. From the critical standpoint, we’ve started to wonder how carefully journalists really listen to the albums when they first come out. Have you ever noticed how many reviews seem to focus on the first two or three songs?”

If Wilco has been knocked for being only an excellent refinement, rather than a mind-blowing breakthrough, the band’s recent DVD, Ashes of American Flags, is arguably one of the best concert films ever. It’s also a nifty encapsulation of the group’s basic set list in recent years (and how could we live without “Handshake Drugs” or “Impossible Germany”?), spread out over a number of U.S. cities, with quirky travel footage and insightful commentary along the way.

“Because I play with the band, I suppose I was slightly more interested in the peripheral aspects of the film,” Stirratt muses. “The settings and the little touches along the way really meant a lot to me, with visits to the parts of cities that everyone forgets. Plus those sunrise moments on the bus, which we don’t really encounter that much anymore. We don’t stay up all night like we used to!”

For Stirratt, that cinematic tour had the bonus of culminating in his hometown, New Orleans.

“It was great to be back at Tipitina’s again. That was where I saw many, many great rock shows when I was young, and they always seemed bigger than life: the Ramones, Hí¼sker Dí¼, and of course all that amazing New Orleans talent. The place seemed so huge, but then, when we actually got to play there, we couldn’t fit everybody on-stage; we had to put part of the band in the balcony!” he says of the travelling horn section known as the Total Pros.

Over the years, Stirratt has also co-led bands such as the Hilltops, with his twin sister, Laurie, and the Autumn Defense, alongside Pat Sansone, Wilco’s elfish jack-of-all-instruments. Like his main employer, the 42-year-old bassist has absorbed every influence from the Beatles to ’70s glam and folky Americana.

“I’m a veteran of this whole Southeast scene, from Louisiana east; there were hundreds of these little dives where all the ’80s bands played. Black Flag and Fugazi and Superchunk would come through every town. It was pre-alternative and it was a rich time for music, even in the backwaters.”

Despite its down-home virtues, the Integrity Circuit had its own peculiar perils.

“In the early ’90s, there was a feeling that if you had a hit, you were over. The flameout potential was really high. I guess we were incredibly lucky, because we signed to Warner Brothers early on and we were really nurtured along. I don’t think that could have happened even a little while later.”

Even with long-term label support, it took a while to reach Foxtrot’s crystallization of the band’s capabilities. Intense conflict marked that watershed album, including Wilco being dropped by one division at Warner Records and then being picked up by another. Reflecting on the record, Stirratt says he felt the clouds break when mixer, producer, and guitarist Jim O’Rourke got involved.

“After a year and a half of trying 10 different approaches to every song, his take on the music just made my jaw drop to the floor. I knew instantly that this was the path we needed to take.”

Foxtrot was also the moment when tireless drummer Glenn Kotche came aboard, and Wilco’s rhythm section really clicked.

“We’re much more focused now,” Stirratt says. “We’re better players with better ears and, frankly, we just don’t have as much time to waste anymore, in the studio or anywhere. So I guess you could say we’re starting to know what we’re doing.”

And maybe that matters even more than mattering.

Wilco plays LiveCity Yaletown on Saturday (February 13).