The group's debut album went gold in the UK and America, but Wes admits he had moments when he doubted they would make it.
"When you believe in something really strongly and the rest of the world does not see it the same way, you are forced to look in the mirror and ask: 'Am I crazy'?"
"I was about 20, washing tables and thinking 'maybe I am a fool, maybe the music is not as good as I think'," says Wes. "But we persevered – it took about eight years for us, but there are always dark moments where you think, 'maybe this is not for us'."
It is a sign of the band's success that last year they supported the Civil Wars at the O2 Academy. Now, months later, they are gearing up to headline the same venue.
Originally formed in New York, Wes and drummer Jeremiah Fraites decided to move to Denver to expand their horizons.
That was where they added cellist Neyla Pekarek, and started regularly gigging, eventually developing the sound that was heard on last year's debut album.
Yet when it comes to performing live, they take their chief inspiration from a certain New Jersey legend, especially as they adjust to playing larger venues.
"If you see a Broadway show and everyone is very expressive, the reason for that is because the guy way back in the last row can't see your face," says Wes, a New Jersey native.
"So you have to exaggerate, whereas if you watch a movie they can be more subtle. I remember seeing Bruce Springsteen in a stadium and I was in the last row, yet it felt like I was right next to him. I was fascinated by that, and that is the goal to set."
Yet there can be a price to pay for all the success. All the added media attention, the pressure of playing bigger shows and suddenly finding yourself nominated for a Grammy can be hard to take in, and Wes admits one concern for the band is ensuring they keep their heads in the right place.
"You want to make sure everyone is doing all right, and that all the success is not at the expense of their mental health," he says.
"It can be pretty demanding, especially on your loved ones. I would love to see it grow and get bigger, and the idea that the music can reach as many people as possible appeals.
"We just have to be careful that everyone is all right, because it is not worth it if you are mowing people down along the way."
Wes points to two reasons for the band's popularity. He feels there has been a natural reaction to how slick a lot of modern pop has become, and that The Lumineers have been boosted by the likes of Mumford & Sons suddenly becoming trendy.
"Part of the roots revival is that people are searching for something they can wrap their arms around," he says. "They want to stick their hands in the muck and feel the actual texture of the music because when it gets so sanitised and cleaned up it loses something.
"The style of these records taps into that, but there is also an element of right time, right place, right band. We are a beneficiary of having bands like Mumford & Sons around."
The immediate focus is on the upcoming tour, while they are also recovering from a performance at the Grammys last weekend, performing the hit single Ho Hey.
Says Wes: "Playing on the show, that snowball effect of going from obscurity to the Grammy – that is how absurd the whole thing has become..."
l The Lumineers, O2 Academy, Monday, £10, 7pm.