London (CNN Business)Having negotiated agreements of sorts on trade with China, Mexico, Canada, South Korea and Japan, President Donald Trump is now turning to his next target: the European Union.

Trump made clear at the World Economic Forum in Davos, Switzerland, this week that his administration will move aggressively to negotiate a trade deal with Brussels. And if progress isn’t made quickly, he’ll impose tariffs of up to 25% on cars made in the European Union.

“I wanted to do China first. I wanted to do Mexico and Canada first. But now that we’re all done … we are going to do Europe,” he said during an interview with CNBC on Wednesday.

There may be a deal to be done.

Ursula von der Leyen, the president of the European Commission, met with Trump in Davos, where both leaders pledged to work quickly toward a deal. Von der Leyen told German news agency DPA that an agreement could be reached within weeks.

The transatlantic relationship produced $1.3 trillion in total trade in 2018, according to US government statistics. Counted together, the 28 countries of the EU were the biggest export market for US goods that year.

Yet experts say that aiming for a quick deal means there won’t be time to address thorny issues that have for decades prevented the United States and the European Union from completing a comprehensive agreement to boost trade. The latest effort, the Transatlantic Trade and Investment Partnership, was declared obsolete before it could be finalized.

What sunk the sweeping deal? Activists in Europe were alarmed by the prospect of imports of American genetically-modified crops and meat treated with hormones. The election of Trump, who campaigned in 2016 against new trade agreements, was the final nail in the deal’s coffin.

Chad Bown, a senior fellow at the Peterson Institute for International Economics, said the outline of a new deal is unclear, but it could eliminate some big regulatory barriersto increased trade such as a European limit on the maximum size of trucks. Europe could also modify standards that would allow more US agricultural products to be exported to the continent.

But any deal negotiated in just weeks or months won’t address the toughest issues.

“In a short period of time, I think it’s really unlikely that you would be able to tackle the really big agricultural disparity issues between the United States and the European Union,” said Bown.

The Trump administration may instead choose another option from its playbook. Since becoming president, Trump has entered negotiations with South Korea, Canada and Mexico that resulted in tweaks to existing trade deals. Talks with China resulted in a “phase one” deal of narrow scope. Japan has also been convinced to sign a limited trade pact in order to avoid new tariffs.

Could he do the same with the European Union?

“With Europe, it’s different. We’ve never come to a full agreement with them on any deal,” said Bown. “So it’s a really big unknown what they’re going to piece together, and actually put into this thing, and call it a trade agreement.”

In recent days, Trump has renewed his threat to hike tariffs on cars made in Europe to 25%.

“Look, if we don’t get something, I’m going to have to take action, and the action will be a very high tariffs on their cars and other things that come into our country,” Trump said during his interview with CNBC in Davos.

Doing so would strike at the heart of European industry, making cars produced by Volkswagen(VLKAF), BMW(BMWYY) and Daimler(DDAIF) in their home market more expensive for Americans to purchase. Germany, where manufacturing is mired in recession, can scarcely afford new taxes on its products. But the blowback would also likely dent growth in the United States.

“It would certainly have very significant negative implications” for economic growth both in Europe and the United States, said Torsten Slok, chief economist at Deutsche Bank Securities.

Much would come down to the details, and whether the United States decided to tax completed cars, auto components or both.

There is a risk for miscalculation, according to Bown.

“Europe is not Japan. Europe is not China,” he said. “If Trump does auto tariffs on Europe, there is a real sense that the political calculus in Europe would change … and they would be forced to retaliate, and they are an economy of equal size.”

Still, the threat may be enough to bring Europe to the negotiating table.

“The European Union is probably thinking, ‘Hey if we can find something to give them, and that keeps tariffs on cars off the table, it makes sense to move forward,'” said Sam Lowe, a senior research fellow at the Centre for European Reform.

German Chancellor Angela Merkel, speaking Thursday in Davos, said she hoped a deal could be done with the United States, while reiterating her view that a multilateral trading framework was a better route to global prosperity.

Even a small deal with Europe could be a powerful tool for Trump on the campaign trail. In Davos, the president offered a preview of his reelection pitch to the American people, arguing that his trade deals have boosted the US economy and produced jobs.

“The president, we know, has a history of putting together really small deals and calling them momentous trade agreements,” said Bown. “So what he’s going to call a trade agreement in this context, we’ll have to wait and see.”

Julia Horowitz and Mark Thompson contributed reporting.