(This post has been updated.)

During the 2010 midterm campaign, the tea party had emerged as a fully formed oppositional force to Democrats and so-called establishment Republicans alike. On Capitol Hill, congressional Republicans were determined to limit President Barack Obama’s victories and had managed to turn the bitter health-care debate against Democrats.

In the midst of all that emerged a group of ideologically middle-of-the-road politicians who wanted to cut through the dysfunction paralyzing Washington with bipartisan solutions. They called themselves “No Labels,” and their proudest accomplishment to date might be that in 2012, they persuaded members of Congress to invite someone from the other party to sit with them at the State of the Union, high school prom-style.

In 2013, on a sweltering summer day, the group held a rally outside the Capitol where they announced that dozens of lawmakers had declared themselves “Problem Solvers” and committed to the aspirational goal of ending Washington gridlock. Several months later, the government shut down.

The problem with the Problem Solvers is they haven’t actually solved anything.

So now, in their latest grasp at relevance, some Democratic members of the caucus are holding hostage their support for Minority Leader Nancy Pelosi (D-Calif.) for Speaker of the House over demands born out of their bipartisan Problem Solvers caucus.

Members of the Problem Solvers can be as evangelical about being nonpartisan as they say those on the partisan extremes are about their positions. At a congressional debate in a suburban Philadelphia district, incumbent GOP Rep. Brian Fitzpatrick, who often espouses the virtues of being a Problem Solver, asked his opponent to please stop referring to him as a “Republican.”

“Scott, I’m hearing you throw the word Republican out,” Fitzpatrick told Democrat Scott Wallace. “Do your best to try to keep party labels out of the debate, because really it’s important. Okay?”

There are 48 members of the Problem Solvers, and there is an even split between Republicans and Democrats (new members must bring in a buddy from the other party to maintain the even split). This year, they released bipartisan legislation on gun control, infrastructure, health care and immigration. A rule of the group is if 75 percent of the caucus as well as a majority of both Democrats and Republicans in it agree on a proposal, it becomes the caucus’s official position.

Now, to help their ideas gain traction, the group wants Pelosi to commit to certain House rule changes that would make it easier to get hearings and floor votes for bipartisan measures and thus increase the likelihood they get picked up by the GOP-led Senate. Otherwise, they argue, Democrats will pass their bills in the House, Republicans will pass theirs in the Senate, and Washington will remain at a legislative standstill.

“The American people want Republicans and Democrats to work together to solve our country’s problems," said Rep. Tom Reed (D-N.Y.) in a statement. “The move to change the House rules isn’t about politics, it’s about Congress being a top-down driven organization where you work hard to acquire bipartisan consensus on legislation and you’re told ‘no’ -- the rules of the House say no you can’t even get an up or down vote unless the Speaker blesses the bill.”

The group’s demands would essentially dilute Pelosi’s power by forcing her to cede some control over setting the floor agenda. The Problem Solvers are demanding any bill co-sponsored by three-fifths of House members and any amendment with at least 20 Democratic and 20 Republican co-sponsors gets a debate and a vote.

The Problem Solvers promote functional governing as their motivation, but their mission is also about self-preservation. Its members on both sides of the aisle tend to be moderates who represent swing districts and are most vulnerable in any given election cycle. Much like the far-right Freedom Caucus did no favors to the more moderate Republicans with their intransigence, Democrats warn that the Problem Solvers Caucus, too, could be kicked out of office if the party tilts too far left.

Former senator Evan Bayh (D-Ind.) said as much in an op-ed in the Hill:

These reforms represent the only realistic opportunity you will have to steer the House toward an agenda that will keep you in good stead with the voters who supported you, but likely supported your opponent two years earlier. Absent these reforms, you’re likely to face a re-election fight in which you have to defend a congressional agenda crafted almost entirely by more senior Democrats who are more interested in sticking it to the other party than in forging bipartisan solutions. In other words, the debate we’re about to have on the rules of the House may well determine the contours of the campaign you’ll be compelled to run in 2020.

With only 24 members belonging to the Democratic majority, the Problem Solvers may have a hard time driving the agenda in the next Congress. Which is why they are picking this fight with Pelosi. They say changing the way the House operates is their only chance at getting their priorities taken seriously.