A surprisingly good jobs report on Friday has sharpened questions about what kind of influence the economy will have on the 2020 presidential election.

The official unemployment rate for May was 13.3 percent, down from 14.7 percent the previous month, the Bureau of Labor Statistics announced. The new figure is much better than expectations yet still much worse than the nadir of the Great Recession more than a decade ago.

The complicated dynamic poses challenges both for President Trump and for his presumptive Democratic challenger, former Vice President Joe Biden.

Trump has already begun celebrating the job numbers. But, in doing so, he could end up sounding a note that appears too euphoric, and therefore out of step with the millions of Americans who have been thrown into unemployment in recent months.

The reverse is true for Biden. He argued Friday that missteps by Trump in handling the coronavirus crisis have deepened its economic impact — and that the president is prematurely declaring victory. But if he goes too far in that direction, Biden leaves himself open to the charge that he is talking down a recovery — or even rooting for continued economic suffering as a tool that would help lever Trump out of the White House in November.

Even some Democrats are expressing concern about whether their party’s response to the unexpected economic news will strike the right tone.

Hank Sheinkopf, a Democratic strategist in New York, argued that Democrats would be better advised to make the argument that they had helped put the nation on the road to recovery than simply “attacking Trump head-on.”

The latter option “looks partisan, and it goes back to his argument” that Democrats have acted in an obstructionist way, Sheinkopf said.

By contrast, a focus on the Democratic push for legislation to ameliorate the worst impacts of the crisis would be far more effective, he argued.

“The message needs to be: ‘We passed the stimulus bill to get people working again. It was the right thing to do, and we should have done more, which would have brought the unemployment number down even more. But we had to work against [Senate Majority Leader Mitch] McConnell and Trump to get that done.’” Sheinkopf said.

Trump, meanwhile, is making every effort to take advantage of the jobs surprise — especially coming off a period when his approval ratings have slipped, he has fallen behind Biden in head-to-head polls and the nation has been roiled by protests following the killing of George Floyd.

Trump noted on Friday that some experts had predicted unemployment could rise as high as 20 percent in May.

After a flurry of celebratory tweets, Trump also held an event in the White House Rose Garden on short notice. There he asserted that it was only a matter of time before “we will go back to having the greatest economy anywhere in the world — nothing close.”

Trump also suggested that the speed of the recovery could be even better than the rosiest previous predictions.

The president alluded to the hope that there could be a quick bounce-back, often termed a “V-shaped recovery.”

“This is better than a V, this is a rocket ship,” Trump insisted.

The characteristically hyperbolic phrase could backfire if it lands badly with those millions of Americans left behind by the “rocket ship” however.

The administration’s emphatic response to the May employment report — “this recovery begins today,” Vice President Pence told CNBC — could also leave Trump politically exposed if the recovery proves halting or weak.

Former President Obama’s administration suffered a setback of a roughly comparable kind a decade ago, having labeled mid-2010 “recovery summer” following the seismic shock of the financial crisis and Great Recession.

No real recovery took place — the unemployment that year was 9.6 percent in May and 9.5 percent in September — and the slogan was quietly abandoned.

Republicans are already arguing, however, that the significance of the new data is that it shows a corner has been turned.

“There could be a month [between now and the election] when there is going to be less job growth than in the other months,” said Republican strategist Ron Bonjean. “But it’s highly unlikely that we are going to have two or three months of job growth and then a month of job losses. I’ve never seen that happen. The key here is to have the trend moving in a positive direction.”

Trump has at least one advantage. Opinion polls have consistently shown his performance on the economy winning broader approval than his handling of other issues. An Economist/YouGov poll released this week found 50 percent of adults approving of his handling of the economy, even as his overall job approval rating was a full 10 percentage points lower.

Biden, meanwhile, sought to highlight the scale of the problems still facing the U.S. in his remarks on the new job numbers.

“I was disturbed … to see the president crowing this morning — basically hanging a 'mission accomplished' banner when there is so much work to be done — and so many Americans are still hurting,” Biden said Friday. “For an enormous swath of our country, their dreams are still on hold. They are still struggling to put food on the table. The unemployment rate remains the highest it’s been in nearly a century.”

Those factors could easily deliver the White House to Biden. More than 40 million new jobless claims have been filed since the coronavirus crisis began, and the job growth in the new numbers was only about 2.5 million.

Trump could also be undone by any number of other factors, including any resurgence in the coronavirus crisis, public dissatisfaction with his response to the current protests or simple voter fatigue with his tempestuous personality.

But, for now, even Democrats are newly aware of the dangers of counting him out.

“If people think he can’t win, they are deluding themselves,” said Sheinkopf, the Democratic strategist. "He could be reelected. He lives and dies by these economic numbers.”

The Memo is a reported column by Niall Stanage, primarily focused on Donald Trump’s presidency.