On Capitol Hill, the leaders of a deeply unpopular Congress have begun to talk about doing something radical.

Agreeing with one another.

In anticipation of President Obama’s address to Congress on jobs Thursday night, leaders in both parties have already identified a few jobs-related bills that could pass both the GOP-led House and the Democrat-held Senate in the coming months.

To agree on any of them would mark a significant change in tone for this divided Congress. So far, Republicans and Democrats have cut deals only when they absolutely had to stave off a disaster, such as a government shutdown or national default.

“We have to focus on areas of commonality and try to transcend differences here,” House Majority Leader Eric Cantor (R-Va.) told reporters Wednesday. “We need to build consensus, and that is going to require us all not to impugn motives or to question patriotism. We have a job to do.”

The prospect of more cooperation is a hopeful sign, but an examination of the bills favored by both parties shows that they are too small-bore to solve the country’s vast problem with unemployment. Several only reauthorize existing programs and are unlikely to give the economy a new boost.

The most positive impact, economists said, might not be what these bills do for the economy, but what they do for Congress itself if they allow a skeptical country to see Washington working together rather than just fighting.

“For them to show their constituents that they can actually work together and pass some measures . . . is positive,” said Jared Bernstein, a former member of President Obama’s economic team who is a senior fellow at the Center on Budget and Policy Priorities. “Does it go far enough? Not by a long shot. But at least they’re not shooting themselves in the feet.”

Still, change is hard. In the few days since Congress returned from its August recess, Democratic and Republican leaders in the Senate have gone right back to sniping at one another. In the House, the number-two Democrat said he thought the lack of job creation was mainly Republicans’ fault — for forcing showdowns that brought Congress twice to the brink of disaster.

“The Republicans talked a lot in the last Congress about how certainty was important to the business community. I think they were right,” Rep. Steny H. Hoyer (D-Md.). said. “They have spent the year adding to uncertainty.”

But leaders and their aides believe that there is room for these people to agree. The list of potential compromises on jobs, compiled from interviews with Republican and Democratic aides, begins with an extension of a federal payroll tax “holiday.”

That involves reducing the tax that employees have taken out of their wages to fund Social Security, from 6.2 percent to 4.2 percent. That reduction is already in place for 2011: The administration says it saves the average family about $1,000.

Now, Obama has suggested extending it through 2012. Congressional Democrats are on board — and Cantor said Wednesday that he had supported the idea in the past.

The idea is that more money for workers means more spending by workers. Which means more jobs, to make the things they want to buy.

But this year, that equation isn’t working out as planned. Despite the existing tax “holiday,” job growth slowed to zero in the last quarter.

“If a payroll tax cut is the best thing we have got left, we are in trouble,” said Andrew G. Biggs, a resident scholar at the American Enterprise Institute who studies economic policy. “We’ve already had the payroll tax cut. And does the economy seem to be improving?”

Another idea with bipartisan support is the approval of new trade agreements with South Korea, Colombia and Panama. Both President Obama and House Republicans say that lowering trade barriers would mean new markets for U.S. goods — and new jobs to supply those markets.

The holdup, for now, is over a federal program that provides aid for U.S. workers who lost jobs because of imports or overseas competition. Democrats want the program, which expired in February, to be reauthorized, while Republicans criticize the program as ineffective and costly.

If the two sides can agree, the White House estimates that the Korea deal could “support” 70,000 U.S. jobs from increased exports. But other economists warn that the benefits of trade deals can take years to materialize.

“These are things that need to get done — because if they don’t get done, it’ll cost lots of jobs,” said Mark Zandi, chief economist at Moody’s Analytics. He meant that other exporters, such as Canada or Europe, could move into the same markets if the U.S. deals weren’t signed. “But it’s not going to be the answer to our problems.”

The House and Senate also seem close to an agreement on overhauling the country’s patent-review process.

The idea is to allow inventors to get patent approval faster, which would help get fledgling companies off the ground sooner. But this measure, also, could take years to pay off with significant new jobs.

Party leaders are also optimistic about a bill to fund the Federal Aviation Administration, and another for construction and maintenance of U.S. highways. But both snagged in inter-party disputes.

The FAA bill is held up by a fight over the right of airline workers to unionize. And the highway bill is the subject of a disagreement over how much it should spend.

And even if they passed, it’s not clear how many new jobs either bill would add. Because overall funding in the two bills is not likely to increase, said Janet Kavinoky of the U.S. Chamber of Commerce, the government’s only hope would be to spend its money far more efficiently.

Which might be even more of a long shot than finding agreement in Congress.

“We might be able to keep the ailing construction sector propped up” with current funding levels, Kavinoky said. But, she said, without major improvements in the efficiency of government projects, “you’re not going to see major job creation.”

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