The U.S. Senate has a gang problem.

To tackle immigration, senators formed a Gang of 12. On energy policy, they tried a Gang of 10 ( which became a Gang of 20). Now, under pressure to lower the national debt, Congress is waiting for a bipartisan plan from a Gang of Six.

Those are the gangs. This is the problem: Often, they don’t work.

The gangs of 12, 10 and 20 all failed. So did the Senate’s last Gang of Six , which sought bipartisan agreement on health care in 2009.

These informal groups are intended to create breakthroughs, in a Senate paralyzed by odd rules and polarized parties. But they usually fizzle out, because the Senate is paralyzed by odd rules and polarized parties.

This week, the newest gang was already dragging its feet. So the Senate may be on the verge of re-learning a lesson that it never seems to remember.

“It’s soothing to believe that these seemingly intractable problems can be at least addressed by people of goodwill, working together” in gangs, said Ross K. Baker, a professor of political science at Rutgers University.

“Even though they can’t be,” he said.

The current Gang of Six — three Republicans and three Democrats — has been working together for months. Its goal is to to forge a compromise on the most divisive issue in today’s Congress: how to reduce the deficit and the ballooning national debt.

On Thursday, gang member Sen. Kent Conrad (D-N.D.), chairman of the Budget Committee, said the group’s talks remain on hiatus while another member, Sen. Tom Coburn (R-Okla.), is out of town tending to a family emergency.

Conrad is one of the Hill’s most committed gang members. He participated in the Gangs of 10 and 20, as well as the Gang of Six on health care. But he said he was “quite optimistic” that this group could succeed where others had faltered.

“There have been mixed results, that’s for sure,” he said in a telephone interview. But Conrad said the circumstances demanded forming a new gang (Conrad calls them “groups”). He said the debt demanded a real solution — and in a divided Congress, a solution could only come from a bipartisan agreement.

“There’s a growing consensus that failure is not an option,” Conrad said.

While his group works, House Republicans and President Obama have already proposed their own separate budgets, and Vice President Biden is leading another bipartisan work group of legislators.

Gangs like this one are a product of the Senate’s independent ethos. The House functions like two choirs: party leaders pick the music, and their members generally line up and sing. The Senate, on the other hand, acts more like 100 soloists, each feeling free to make his own alliances.

A “gang” is usually an alliance focused on a specific issue, which forms outside the Senate’s party structures. The media nickname for these groups is new, taken from the “Gang of Four” that helped rule China in the 1960s and 1970s.

But the idea is an old one. In 1860, for instance, a bipartisan “Committee of 13” senators set out to find a compromise that would stave off the Civil War.

“And they failed,” said Don Ritchie, the Senate’s official historian.

Not that there haven’t been successful gangs. In the 1980s, there was the Gang of Five, Republican senators who pushed President Ronald Reagan toward more environment-friendly policies by threatening to vote with Democrats.

And in 2005, a bipartisan Gang of 14 defused a Senate showdown over some of President George W. Bush’s judicial nominees. The gang members said they wouldn’t vote for extreme measures planned by Republicans or Democrats: They forced a compromise in which some judges were confirmed.

But it has been far harder for gangs that want to produce, not just block. They often seek to make back-channel connections between the two parties, circumventing committee chairmen and party bosses who are too caught up in partisan fighting.

The problem is that when they’re done, the chairmen and bosses and partisan fighting are still there.

“The very reason that they’re necessary,” said Steven Smith, of Washington University in St. Louis, “is the same reason why it’s unlikely that they’ll succeed.”

In 2007, the Gang of 12 tried to fashion a grand compromise on immigration. Their plan died after bipartisan opposition. In 2008, the Gang of 10 was working on an equally grand compromise on energy: It might have included expanded offshore drilling (for Republicans) and limits on oil industry tax breaks (for Democrats). The group grew to 20, but their plan was shelved during election-year battles over high gas prices.

In 2009, Sen. Max Baucus (D-Mont.) convened a bipartisan Gang of Six on health care. After months of meetings, it became a gang of nobody; the members couldn’t agree. Baucus released his own plan, and the debate dissolved into bitter partisan fighting.

So why do they keep trying?

“These smaller groups do work. Even though they don’t work, in a formal sense,” said Sen. Jeff Bingaman (D-N.M.), a veteran of the 2009 version of the Gang of Six. He said gangs provide a more intimate setting to discuss policy ideas, and that some of the gang’s ideas survive and make it into law. “You can get a lot more done than you can through a formal hearing process.”

Political scientists see other, less flattering rationales. They say that serving in a gang looks good, even if the gang goes nowhere: it makes a senator appear to float above the unpopular clatter of partisan bickering.

Most members of the current Gang of Six — Coburn, Mark Warner (D-Va.), Richard J. Durbin (D-Ill.), Michael D. Crapo (R-Idaho) and Saxby Chambliss (R-Ga.) — declined to comment this week about why they chose to join another gang.

The task they’ve chosen now is one that makes even the Senate’s most hardened veteran gang members leery.

In the past six years, Sen. Ben Nelson (Neb.) a conservative Democrat, has joined gangs of 10, 14, 16 and 20. But, looking at this gang from the outside, he wonders if the debt is just too vast a subject for any six senators to tackle on their own.

“That may be too big for Congress in general,” Nelson said, “not just a gang.”