They’re calling it “the record that just won’t die.” It’s more like, “The little record that could.”

A full year since the release of their A&M debut album, “New Miserable Experience,” the Gin Blossoms are hotter than the scorching pavement on the streets of their native Tempe, Ariz.

The album, having sold more than 350,000 units, is poised (and climbing) at No. 71 on Billboard’s Top 200 chart. The jangly pop hit “Hey Jealousy” is at No. 77 with a bullet on the Hot 100; the video is on MTV’s Buzz Bin rotation, and better still, the rock quintet is getting tremendous exposure as the opening act for UB40’s North American tour.

“It’s been a really weird climb,” groggy-voiced bassist Bill Leen said over the phone from a Boston hotel room. “We haven’t had any big jumps. We’re just taking one step at a time up the ladder of success, or whatever you want to call it.”

“New Miserable Experience,” recorded at Ardent Studios in Memphis, was released on Aug. 4, 1992. It was greeted with favorable critical response, with some hailing the Gin Blossoms as “a cross between the Byrds and Husker Du” and “the sons of Petty and R.E.M.”

But it appeared they would remain only a regional fixture. “Hey Jealousy” died the first time around, and the followup single, “Mrs. Rita,” didn’t fare much better.

Leen, lead singer Robin Wilson, guitarist Jesse Valenzuela, drummer Phillip Rhodes and guitarist Doug Hopkins did what young struggling artists do to get attention: played nearly 200 shows in the last 12 months. Their diligence paid off with an appearance on TV’s “Late Night With David Letterman.” Dave was so impressed, he called them back a few months later for a flattering encore.

For Leen, it seems like ages ago when the Gin Blossoms formed in 1987 and made their mark on the Tempe club scene. Their self-produced independent album, “Dusted,” solidified a loyal following and later earned them a spot on MTV’s New Music Awards as “the best unsigned band.”

The “unsigned” tag didn’t last long. The big labels soon came courting, with A&M winning the bidding war in 1990.

Now, after months of touring in a cramped van and trying to recoup nearly $500,000 in expenses, the Gin Blossoms can finally see light at the end of the tunnel. They’re now tooling around in a “real bus,” Leen said, and no longer need tour support from A&M.

“We’re not exactly starving artists,” he said. “We still pay our rent, and in the old days, sometimes you couldn’t pay the rent. I don’t know, if you could look at my bank book right now, though, you’d be shocked.

“The money is just around the corner, or a little bit more. And that’s fine because we have a plan, and everything has worked out better than we’ve expected, so maybe there will be a little bit of a reward in the future.”

Now, if they could only get beyond “Hey Jealousy.” Leen said they’re anxious to work on a new album.

“We’re bored to death with ‘Hey Jealousy,’ ” he said. “We did it on Arsenio Hall last week, and we were thinking, ‘God, I wish we could do something different.’ … It can get pretty monotonous, because we would like to be able to take some time off and take vacations with our families, and then the five of us sit around and write a whole new batch of songs.”

Leen admits that might be wishful thinking.