Correction: An earlier version fo this article misstated the name of the office headed by Douglas W. Elmendorf. It is the Congressional Budget Office, not the Congressional Budget Committee. This version has been corrected.

The great hunt for common ground on Capitol Hill that opened hopefully with the post-summer session of Congress lasted, in all, about a week.

It began on Sept. 6, with a letter from House Speaker John A. Boehner (R-Ohio) and House Majority Leader Eric Cantor (R-Va.) to President Obama. It asked that the two sides ease their bickering and look for areas to agree on.

By Tuesday it was over.

The congressional “supercommittee” charged with trimming at least $1.2 trillion from the federal deficit over the next 10 years met for its first public hearing Tuesday. Around the Capitol, each side began to drift back to its postures of the past eight months, in which compromise was the other guy’s job.

“That’s going to continue for the next year and a half. I wish I could tell you different,” Rep. Tom Rooney (R-Fla.) said at the end of the day. “This is it.”

The search had begun as Congress returned from an unhappy August recess, in which its approval ratings plunged to historic lows. Cantor and Boehner — the faces of an assertive new Republican House majority — seemed particularly keen to change the tone.

“We’re not going to let our differences get in the way of coming together for solutions that help produce results,” Cantor tweeted on Thursday, the day of Obama’s jobs speech. “Need 2 work 2gether 4 results!” he tweeted later that day, making the same point in 30 characters.

Over the next few days, strange things happened: The hard-driving Cantor became Washington’s chief spokesman for togetherness. The above-it-all president demanded that Congress “Pass this bill.” Supercommittee members spoke optimistically about solving problems that have divided Washington for decades.

The two sides found small areas of agreement, such as tax cuts proposed in the president’s plan. But not much else.

Then, on Tuesday, the supercommittee met to hear testimony from Douglas W. Elmendorf, the director of the nonpartisan Congressional Budget Office.

In their first meeting, the 12 members had seemed hopeful.

But in this meeting, most of them asked Elmendorf some version of an old Washington question: Isn’t it true that my party has been right all along?

“Isn’t it fair to say that, in fact, there is an aspect about our budget today that is starkly different, which is the level of revenues?” said Sen. John F. Kerry (D-Mass.). His point was that tax revenues have been allowed to sink too low, a dig at Republicans.

“Isn’t there a danger that the magnitude of the debt is already impeding economic growth?” Sen. Patrick Toomey (R-Pa.) asked Elmendorf. His point was that the debt had been allowed to rise too high. A dig at Democrats.

At the end, even Elmendorf was gently suggesting that the lawmakers weren’t asking the right questions.

“The fundamental question for you is not how we got here, but ‘Where do you want the country to go?’ ” Elmendorf said. “What role do you and your colleagues want the government to play in the economy and the private sector?”

However hopeful the early signals, they began to fade about the time of Obama’s speech, in which he made sharp demands for Republicans to approve a slate of tax cuts and spending increases. The moves could be paid for, he later said, in part by raising taxes on people with high incomes.

Republicans said they could accept some of those moves, including a cut in payroll taxes. But they held fast against others, including the tax increases on high earners.

Obama sent over the entire package. And, by then, the tone had changed.

“Let us set aside our differences and try and transcend them and come together,” Cantor said Monday.

That wasn’t the change. The change was that Cantor was blaming Obama for not transcending. “That’s why I have taken issue with this all-or-nothing demand by the White House and the president,” he continued. “It is just not appropriate now. It won’t help us to produce results. We have been there.”

At the White House, senior administration officials told reporters that Republicans were the problem. They said that if Obama’s jobs plan doesn’t pass, the president will spend the year hammering on the idea that the GOP was an obstacle to progress.

They predicted that if the economy continues to sputter and congressional approval ratings remain in the teens, Republicans will lose control of the chamber in next year’s elections.

By Tuesday, freshman Rep. Adam Kinzinger (R-Ill.) said he hoped that the week-long experiment had produced some good results — for Congress and the public.

“The Great Common Ground Hunt — you know, it’s a good start,” he said. “It’s at least sending a good image to the American people.”

Boehner said in a news conference that House committees will now consider Obama’s plan piece by piece. White House officials said that the president will sign any part of the plan that reaches his desk, but that he would prefer that the package be acted on as a whole.

A reporter asked Boehner: Is the honeymoon really over?

“Hope springs eternal,” the speaker replied.

Which seemed like his way of saying yes.

On Monday evening, after a day of arguing about Obama’s jobs proposal, Boehner left the House chamber and walked through the Capitol’s Statuary Hall toward his office.

He passed a small light at the base of one statue, where a workman was buffing away the corrosion that tourists’ fingerprints had left on the bronze feet.

The workman would be there until maybe midnight, long after Congress went home. This was the most scuffed-up statue in the hall. It was of Henry Clay, a 19th-century senator from Kentucky, whom people called the Great Compromiser.

Staff writers Felicia Sonmez and Peter Wallsten contributed to this report.