President Obama, left, shakes hands with House Speaker Paul D. Ryan (R-Wis.) before delivering the State of the Union address in Washington on Jan. 12. (Chip Somodevilla/Getty Images)

PRESIDENT OBAMA did not focus his final State of the Union address on an agenda for the next — and last — year of his presidency, tacitly indicati ng that he does not expect to make much headway as a lame duck facing a hostile Congress in an election year.

But the president still noted the flurry of legislative compromise at the end of last year, which kept the government open and provided long-term infrastructure funding. And he reached out directly to House Speaker Paul D. Ryan (R-Wis.):

“Speaker Ryan has talked about his interest in tackling poverty,” he said. “I’d welcome a serious discussion about strategies we can all support, like expanding tax cuts for low-income workers who don’t have children.”

Given the perpetual partisan rancor about the size of the federal safety net, it may be surprising that there is a significant point of agreement between policy minds in both parties on expanding a major anti-poverty program. The success and elegance of the earned-income tax credit (EITC) accomplish this feat. The credit tops up wages for low-income working people, pulling millions out of poverty every year. But its design — increasing the subsidy with wages before flatlining and then tapering off — encourages people to enter the labor force and work more once they are in it. As a means of improving conditions for the working poor, it is much better targeted than, say, increasing the minimum wage, which helps teenagers from affluent families as much as desperate parents trying to feed and house their children.

There are some questions about better- preventing fraudulent EITC claims, but the big problem with the policy is that it is too stingy. It focuses on helping poor people with children, when it should serve as a more holistic response to poverty in the United States, because it helps people and promotes work all at once. Mr. Obama has proposed increasing benefits for poor single people. So has Mr. Ryan, in a nearly identical plan. At the poverty summit Mr. Ryan moderated this month , moreover, other Republicans expressed interest in making EITC reform happen.

So why hasn’t it yet? The sticking point has been how to pay for such an expansion, which would cost about $6 billion per year. In the past, Mr. Obama has proposed raising taxes a bit on certain wealthy people, whereas Mr. Ryan has favored taking the money out of other anti-poverty programs he insists are ineffective. For two men of goodwill, this is a bridgeable divide. Money could be raised by mixing the two approaches, or from somewhere else entirely: Commentator Jonathan Chait has suggested linking EITC expansion with adopting the so-called chained CPI, a money-saving reform to Social Security that would change the way the government calculates cost-of-living adjustments.

The potential for compromise is obvious. Election year or no, Mr. Ryan should take the president up on his offer.