Sen. James Inhofe (R-Okla.), right, and Sen. Barbara Boxer (D-Calif.), center, attend a House and Senate conference on the transportation bill in May. At left is Florida Republican John L. Mica, who is chairman of the House Transportation and Infrastructure Committee. (Susan Walsh/AP)

In a rare conciliatory gesture, two U.S. senators — one a conservative Republican, the other a liberal Democrat — hand-delivered a critical transportation funding plan to their colleagues in the House on Tuesday.

Their symbolic mission was intended as a show of good faith in a Congress where trust has been in short supply. But it underscored the growing desperation of some legislators and construction industry leaders, who have predicted disastrous consequences if funding issues are not resolved before a June 30 deadline.

“The unemployment situation is bad, and it’s only going to get worse if we don’t get this straightened out,” said Jack Basso of the American Association of State Highway and Transportation Officials. “The construction industry is at 14.2 percent, and the actual job numbers are going down.”

In addition to supporting, by one estimate, 2.9 million construction jobs, the proposal is designed to avert an impending funding crisis when the Highway Trust Fund runs out of money in the next fiscal year.

Diplomacy required that the thick document delivered by Sens. Barbara Boxer (D-Calif.) and James M. Inhofe (R-Okla.) be called a proposal rather than a bill, to indicate that it was negotiable. In fact, it was a bill passed by the Senate that they said had been modified to incorporate some issues raised by the House.

“It’s an offer that reflects a lot of their comments,” Boxer said after she and Inhofe visited the office of House Transportation and Infrastructure Committee Chairman John L. Mica (R-Fla.).

She declined to release the proposal. Mica spokesman Justin Harclerode said, “We are taking a look at that proposal and will discuss it with our conferees.”

The transportation bill has provided a case study of a dysfunctional Congress, the failures of those who seek to find a middle ground and the struggle House Speaker John A. Boehner (R-Ohio) has faced in capitalizing on his party’s majority in the House.

Old-timers have peppered the debate with reminders that sustaining the nation’s transportation system always had been a bipartisan effort, even when the two parties were at loggerheads on the burning issues of the day.

The current discord is fueled by a pair of changes that dramatically altered the equation.

One was the elimination of earmarks, the pet projects of individual members that proved to the folks back home that the lawmaker was worthy of reelection. The almost 7,000 earmarks in the last long-term transportation bill were the grease that got it approved.

Without earmarks to protect, members have been liberated to wage battle on matters of principle, such as funding for bike and pedestrian programs or how to pay for urban mass transit.

Some see federal transportation funding in terms of highways and bridges, others believe just as strongly that inner-city light rail systems and bike paths are essential to the mix. That conflict helped derail the House transportation bill when GOP members from urban areas defected to defend mass transit.

The elephant in the room has been there ever since the last major transportation bill passed in 2005, and its presence has loomed larger since that bill expired in 2009, leaving state transportation planners who rely on a federal master blueprint to limp along on a series of temporary extensions.

The pachyderm no one wants to acknowledge is that there’s little agreement on where to get enough money to pay for transportation, and that gets to a much more fundamental divide between the two parties.

Everyone agrees that the traditional source of transportation funding — the Highway Trust Fund, which is bankrolled by the federal gas tax — is projected to run out of money. All those temporary extensions have dipped into the general fund for support.

Nobody pretends that the Senate bill in conference provides the long-term answer. It cobbles together money from a variety of sources — draining a couple of funding wells that can’t be revisited — for a two-year bill. In the past, long-term transportation bills covered five or six years.

Everyone says that the two-year bill buys time for the fractious Congress to find a better funding solution, but there’s little evidence that it will be able to achieve in the next 18 months what it hasn’t done since 2009.

The prospect of raising the 18.4 cents-per-gallon gas tax draws a bipartisan chorus of boos. Mutterings about charging tolls throughout the interstate highway system send members of both parties to the barricades. And the Republican proposal to raise revenue by opening new territory in the arctic and offshore to oil exploration has drawn skepticism and push back from environmentalists and many Democrats.

The House bill, crafted with major reforms and streamlining of the federal system, went down in flames within weeks this year as the urban-rural schism split Republican ranks. Rather than see his members tarred by charges of ineptitude, Boehner found a way to punt. He had the House pass yet another temporary extension, sending it to the conference committee to be married to the bipartisan two-year Senate transportation bill.

The maneuver allowed for negotiation in conference over the Senate bill.

Staff members have been meeting in private discussions for weeks, and lawmakers also are said to have attended some sessions in droves. The public rhetoric that has emerged has been more of the same.

Boxer and the Democrats say they are open to compromise on anything they think will win ratification in the Senate. House Republicans say the Senate hasn’t been willing to negotiate or been open to the serious reforms they propose.

“We will move the Senate bill as close to the House bill as we can without tanking it,” said a senior Senate committee staff member, who called the Boxer-Inhofe visit “a respectful gesture” to the House. “It's not every day that senators go over to the House to deliver a bill.”

Basso’s organization joined other major transportation groups and 50 local chambers of commerce, traditional Republican bastions, in pressing for final approval of the proposal delivered by Boxer and Inhofe.

The White House piled on the pressure Saturday in President Obama’s weekly radio address.

“Congress should have passed a bill a long time ago to put thousands of construction workers back on the job rebuilding our roads and our bridges and our runways,” the president said.