The debate on Capitol Hill over expired unemployment benefits is putting a spotlight on the still-rough labor market. The nation’s unemployment rate may be ticking closer to the Federal Reserve’s threshold of 6.5 percent, the point where the central bank will reassess its historically low interest rates. But even as the central bank has started to ease back ever so slightly on its economic stimulus program, economists from both sides of the political aisle say the jobs crisis sparked by the 2008 financial meltdown is far from over.

But just what Congress and the Fed can and should do about the sluggish employment market remains the subject of intense disagreement on and off the Hill. As the Federal Reserve ushers in a new era under the chairmanship of Janet L. Yellen, who won Senate confirmation on Jan. 6 and will take the helm of the Fed on Feb. 1, the labor market is likely to remain at the forefront.

Friday’s jobs report only added fuel to the debate: the unemployment rate ticked down from 7 percent to 6.7 percent, but two-thirds of the decline came from the withdrawal of workers from the labor market, and only a third came from the addition of some 74,000 jobs to the market, according to the Bureau of Labor Statistics.

The 6.5 percent benchmark serves as a guide to investors, who can expect that the Fed will be aggressive at least until the data point is met, said William Spriggs, the chief economist for the AFL-CIO. Even after that, the Fed may continue to purchase Treasury and mortgage-backed securities and can leave the federal funds rate on the floor, especially if the rate of inflation continues well below the Fed’s 2 percent target.

Yellen, Spriggs said, “is someone who is driven by numbers. If we get to 6.5 percent and they are still well inside their inflation target, I believe she’ll say, ‘Let’s go underneath that 6.5’” percent target.

The uncertainty comes from the nature of the unemployment rate, which provides only a rough estimate of the state of jobs in America. The rate doesn’t include people who have given up looking for work or those who are working part time when they want a full-time job. The labor force participation rate is just over 62 percent, the lowest since the late 1970s.

Jared Bernstein, a senior fellow at the Center on Budget and Policy Priorities and a former economic adviser to Vice President Joseph R. Biden Jr., said that no one expects the Fed to raise the federal funds rate the minute the official unemployment rate hits 6.5 percent. The target is a “benchmark,” he said, “not an iron-fast rule.”

Given the low labor force participation rate, especially among working-age people, even 6.5 percent “really means something higher than that,” he said.

John Dearie, executive vice president for policy at the Financial Services Forum and co-author of the book “Where the Jobs Are,” said that November marked the “43rd consecutive month during which more unemployed Americans left the workforce discouraged than found jobs.”

Even so, by the end of last year, the economy appeared poised for better growth in 2104. And as the unemployment rate hit 7 percent — and Congress inked a small but significant budget deal — the Federal Reserve’s policy committee decided to scale back its bond-buying program, known as quantitative easing, by $10 billion starting this month.

“At the Fed, they’re not only going to be looking at the unemployment rate; they’re going to be looking at why the unemployment rate is moving and looking at regional differences,” said Mark Calabria, a former senior Republican Banking Committee aide who is now director of financial regulation studies at the Cato Institute. “And they’ll keep an eye on what is Congress doing.”

Calabria added that the Fed probably won’t tighten up its monetary policy, as outgoing Fed Chairman Ben S. Bernanke has indicated, because of worries over uncertainty and new fiscal fights on the horizon.

Republicans have already pledged to seek policy concessions from the White House over President Barack Obama’s request to raise the debt limit this spring.

“There’s a reason to feel that the Fed is probably going to err on the side of liquidity and accommodation longer than they otherwise would have because there’s so much concern about uncertainty coming from Congress,” Calabria said.

The politics of an election year only add to that uncertainty. The issue of jobs is sure to be a hot topic on the campaign trail and already has molded the congressional agenda this year, with a Senate cloture vote on unemployment insurance benefits passing Tuesday and Democrats pushing for an increase to the nation’s minimum wage on the horizon.

Republicans have their own policy measures, such as reducing regulatory and tax burdens on businesses, that they say will help boost the economy and create jobs.

“I think the next year is going to be a series of votes where the Democrats try to distinguish themselves from Republicans with the theme of income inequality,” Calabria said.

Much of it, he said, will feature Democrats playing to their labor union base. “It really is ‘What have you done for us lately?’” he said.

But if the White House and Democrats in Congress will be in agreement with most unions on unemployment benefits and raising the minimum wage, they will most likely find discord when it comes to the Obama administration’s trade agenda, which includes pushing for a renewal of fast-track authority and a sweeping deal known as the Trans-Pacific Partnership.

Trade deals such as the North American Free Trade Agreement 20 years ago and a recent pact with Korea have been a drain on the U.S. economy and have cost millions of jobs, said Kenneth Peres, the chief economist for the Communications Workers of America. The Trans-Pacific Partnership deal, he said, would just continue the “race to the bottom,” perhaps leading to higher unemployment and stagnant wages.

During Yellen’s confirmation hearing late last year, Sen. Charles E. Schumer, D-N.Y., asked the nominee what she viewed as the reasons for growing income inequality in the United States. Indeed, many of the Fed’s critics say the central bank’s policies, such as quantitative easing, have helped bankers and stock-market investors post record profits, while Main Street businesses and ordinary workers have struggled.

“I want to echo my agreement with you that this is a very serious problem,” Yellen told Schumer.

She said the gap had many factors and among them may be “globalization, with institutional changes in the United States, including the decline of unions.”

Peres said he agrees with the correlation about unions.

“If you look at the rise in income inequality, it matches the decline in union density in the United States, especially from the mid-’70s where you had a beginning in a precipitous decline in union membership,” he said. Collective bargaining, he said, is a “way to lift workers’ wages,” which could create more demand for goods and services in the overall economy.

The austerity push by Congress, he said, has made matters worse.

Bernstein of the Center on Budget and Policy Priorities agreed, and he doesn’t expect Capitol Hill to do much to help the employment scene this year. “But I think they might do less harm,” he said.

Between 2009 and 2013, the deficit as share of gross domestic product fell from 10 percent to 4 percent, as Congress tightened the nation’s purse strings in response to the great recession. “That’s the largest four year drop since 1950,” Bernstein said. “There’ll be less of that this year.”

But, he said, if Congress does not extend the unemployment benefits, that will create “more fiscal drag” that could offset the uptick of the budget deal easing some of the sequester cuts.

Peter Colavito, government relations director for the Service Employees International Union, said the unexpected Senate vote in favor of cloture on the unemployment benefits measure “shows how much pain there still is in communities. That’s an indication, when you can break through those partisan walls, how much struggle there is for workers.”