WASHINGTON — Increased hiring, lower unemployment, stock market on the rise. Who gets the credit?

It’s a hotly debated point in Washington, where political scorekeeping amounts to who gets blame and who gets praise.

Following Friday’s strong jobs report — 236,000 new jobs and unemployment dropping to a four-year low of 7.7 percent — partisans hurriedly staked out turf.

“Woot woot!” tweeted former White House economic adviser Austan Goolsbee. “With 12 million still unemployed?” countered Senate Republican leader Mitch McConnell’s spokesman, Don Stewart.

Presidents usually get the rap for economic downturns and reap benefits when things improve. But the main factors affecting the current recovery and the record activity in the stock market may have less to do with high-profile fiscal policy fights in Washington than they do in the decisions of the Federal Reserve Bank, which has pumped trillions of dollars into the economy, kept interests rates at near zero and pushed investors away from low-yield bonds to stocks.

“From a policy standpoint, this is being driven primarily by the Fed,” said Mark Vitner, an economist at Wells Fargo.

Yet to some, Washington deserves little recognition.

“Economies recover,” said Douglas Holtz-Eakin, a former director of the nonpartisan Congressional Budget Office and now head of the American Action Forum, a conservative public policy institute. He acknowledged the Fed’s monetary policies halted the initial free fall by the financial industry, but he said the economy has had to catch up to the Fed’s low interest rates.

“It took a long time for the housing market for them to matter and for the auto market for them to matter,” Holtz-Eakin said. “So I don’t think that’s a policy victory.”

If Democrats are eager to give President Barack Obama acclaim for spurring the recovery with an infusion of spending in 2009, there are just as many Republicans who will claim his health care law and his regulatory regimes slowed it.

If there is common ground among economists, it is that the next step in fiscal policy should be focused on reining in long-term spending on entitlements programs, particularly Medicare, instead of continuing debates over short-term spending. But such a grand bargain has been elusive, caught in a fight over Obama’s desire for more tax revenue and Republican opposition to more tax increases.

Obama and some Republicans are trying to move the process with phone calls and a dinner here and a luncheon there. Next week, the president plans to address Democrats and Republicans in the House and Senate in separate meetings to see, as he put it Saturday in his weekly radio and Internet address, “if we can untangle some of the gridlock.”

Who gets credit does have political consequences. A strong economy would create more space for Obama to pursue other aspects of his second-term agenda. But it’s an important question for the long term, too, because if the recovery is indeed accelerating it could validate the policies that the Obama administration and the Fed put in place.

Hiring has been boosted by high corporate profits and by strength in the housing, auto, manufacturing and construction sectors. Corporate profits are up. Still, it might be too soon to declare victory. While the recovery may be getting traction, the U.S. economy is not yet strong.

Economic growth is forecast to be a modest 2 percent this year. Unemployment, even as it drops, remains high nearly four years after the end of the Great Recession, with roughly 12 million people out of work.

Last year’s early months also showed strong job gains only to see them fade by June.

March could prove to be a more telling indicator as the economy responds to a third month of higher Social Security taxes and as across-the-board spending cuts that kicked in March 1 begin to work their way through government programs. Economists say anticipation of the cuts already caused a downturn in the fourth quarter of last year as the defense industry slowed spending. The Congressional Budget Office and some private forecasters say the coming cuts could reduce economic growth by about half a percentage point and cost about 700,000 jobs by the end of 2014.

“My view is that aggressive monetary and fiscal policy response to the recovery has been a net positive,” said Mark Zandi, chief economist at Moody’s Analytics.

But referring to the automatic cuts, he said, “Fiscal policies have turned from a very powerful tailwind to a pretty significant head wind.” And, he added, “the economy is going to be tested again in the next few months.”

Obama has been distancing himself from the potential consequences of the automatic cuts, even though he signed the legislation that put them in place. Initially, they were designed to be so onerous that it would force all sides to work out a long-term deficit-reduction and debt-stabilization package. But that agreement never materialized.

If the recovery has been slow, White House officials argue, it is because Republicans have been unwilling to yield to Obama’s demands for deficit reduction that combines tax increases and cuts in spending.

Obama himself seemed to touch on that viewpoint in his weekly address.

“At a time when our businesses are gaining a little more traction, the last thing we should do is allow Washington politics to get in the way,” he said while heralding good economic news. “You deserve better than the same political gridlock and refusal to compromise that has too often passed for serious debate over the last few years.”

Vitner, the Wells Fargo economist, argues that if anyone deserves credit for the recovery, it is the American public and American businesses “for being able to tune out all the noise that’s coming from Washington.”

“It’s remarkable,” he said, “that in the face of so much political uncertainty we’ve been able to see the growth that we have.”