With House Republicans laboring to find ground for compromise on a long-term transportation bill, the House on Thursday quietly approved a single piece of legislation to spend money on a bridge that may cost up to $690 million.

It is very much a bridge to somewhere — connecting two Midwestern cities — but it may as well have been the infamous bridge to nowhere from the way Democrats reacted.

“If it looks like a duck, swims like a duck, and quacks like a duck, then it probably is a duck. This is an earmark,” Rep. Nick J. Rahall (D-W.Va.) said when the bill came up for a vote on the House floor.

In that accusation lies a simple subtext to the dilemma that has turned agreement on transportation funding into an unholy mess in the House. For several decades, earmarks were the grease that got big-ticket transportation bills approved.

Derided as pork, they were the very specific projects requested by individual members for their own districts, projects that produced ribbon-cuttings that showed the folks back home that they were doing good work in Washington.

By the time the last long-term transportation bill passed in 2005 — with 6,000 earmarks — the heat was on from critics who said that state officials should decide how to spend federal transportation money, and that it shouldn’t be diverted to pet projects hatched on Capitol Hill.

And by then the fabled “bridge to nowhere” — a $223 million Alaskan project to replace a seven-minute ferry ride to an island populated by 50 people — had come to epitomize wasteful federal spending, forever blackening the term earmark in the national dialogue.

This time around, when the House leadership presented a five-year transportation proposal, it proudly pointed out that there was not a single earmark of any sort in the plan.

They very quickly discovered that arm-twisting and coalition-building is a lot tougher when individual members don’t have hometown projects to protect. Free of parochial concerns, members are more prone to take stands on principle, like the tea party members who want to cut the bill’s overall spending. Or the urban Republicans who broke party ranks to defend funding for mass transit.

Efforts by House Speaker John A. Boehner (R-Ohio) efforts to reshape the bill into a more modest 18-month proposal, one that would restore dedicated funding for transit, appeared to be running into trouble with the majority of his party this week.

Into the midst of this havoc came a bill approved by the Senate in January to build a bridge across the St. Croix River, connecting Oak Park Heights, Minn., (population 4,724) and St. Joseph’s, Wis., (population 3,882). Bigger cities sit behind both riverfront towns, and there’s widespread agreement that congestion on the current 80-year-old lift bridge is intolerable.

Minnesota Gov. Mark Dayton wrote last week to the local congresswoman, former GOP presidential contender Michele Bachmann, saying that if Congress didn’t approve the bill by March 15, the project might be doomed because the state’s contribution would have to be spent elsewhere.

But Rahall raised objection to a single bill for a single bridge, given that an estimated 70,000 bridges nationwide have been deemed structurally deficient.

“What we ought to be doing today is passing a long-term surface transportation bill so we can begin to address the backlog of deficient bridges, roads and transit systems in every state across the nation,” Rahall said. “Instead, we are voting on one earmark.”

The nitty-gritty of House rules leave it to a committee chairman to decide exactly what is an earmark and what is not. With GOP advisers telling him it wasn’t an earmark, House Transportation Committee Chairman John L. Mica (R-Fla.) didn’t step in to stop the bridge bill, and since it was brought to a vote under suspension of the rules it couldn’t be blocked on the floor.

Not that it would have been anyway.

In the paradox and irony of the current Congress, the bill passed easily, 339-80, with bipartisan support, even though some experts on the Democratic side said it clearly was an earmark under House rules.

And Rahall voted for it. He supports earmarks, despite the public’s aversion and current sentiment among his colleagues on Capitol Hill.