With just three weeks on the job, President Donald Trump is still working on his relationship with Senator Chuck Schumer.

Schumer is the classic insider -- rising through the House, and then the ranks of the Senate, to become the most powerful Democrat in Washington. Trump, the outsider, is a tough-talking real-estate developer from Queens who’s never held public office before.

Schumer loves a backroom deal. Trump wrote a book called The Art of The Deal.

But now the two New Yorkers are circling the ring ahead of a no-holds-barred fight to fill a vacant Supreme Court seat — always a main event in the nation's capital.

Democrats are seething and threatening to fillibuster, arguing the seat was stolen from from President Barack Obama when Senate Republicans refused to consider his nominee for nearly a year. Republicans think Democrats should get over it.

The nomination battle could cripple Trump and Schumer's relationship before they have a chance to talk deals, for instance, on infrastructure or changing taxes on investment profits. Those who know them both — like New York Republican Party chairman Ed Cox — say Trump and Schumer can build a partnership from discord.

“I can see two New Yorkers," Cox said, "actually getting things done despite that kind of tension. That’s a creative tension if properly managed.”

But so far their relationship has been a moving target, and there’s not a lot of history that sheds light on how it will evolve.

Trump has bragged that he was “close to Schumer in many ways” and he contributed to Schumer’s campaigns over the years. And led by Schumer, Senate Democrats raised $230,000 at a 2008 fundraiser at Trump’s Palm Beach mansion.

But Schumer says the president is not his friend.  Manhattan power lunches or rounds at Trump National were not on the schedule.

Aides say Trump and Schumer have been in regular contact since Election Day. The two had three face-to-face encounters during Trump’s first week as president, including a meet-and-greet with Congressional leaders and a chat about Trump’s Supreme Court pick.

Queens Democrat Joe Crowley said that shouldn’t be a surprise, because Trump wasn’t very involved in New York politics. Crowley, chairman of the House Democratic Caucus, said he’s only met Trump four times.

“I’ve never considered him a father of New York City," he said, "or someone who has given back to the city in a major way.”

While Schumer came up through the ranks, Trump campaigned on his business experience and success. He proudly says he made money by strong-arming investors or forcing contractors to accept less pay.

Steven Blader teaches a course on conflict, collaboration and negotiation at New York University’s Stern business school, and he uses Trump as an example in his class. Blader said Trump puts people on the defensive. In a negotiation, that can cause both parties to miss the best possible outcome.

“His mindset that good negotiations are about being domineering and aggressive is counter to exactly what we know to be the case when it comes to negotiation, where you’re far better off mixing collaboration and competition together,” Blader said.

Blader said Trump and Schumer can probably get more done if they avoid treating each other as obstacles and do a little horse-trading instead.

Virginia Republican Eric Cantor knows how that goes. He was House Minority Leader back in 2008, at the height of the financial collapse, when Democrats controlled both houses of Congress and Barack Obama had just became president. Cantor said he presented Obama with reasonable ideas to jump-start the economy — and crossed his fingers.

“Senator Schumer’s been around a long time," Cantor said. "He’s certainly understands policy implications, political sensitivities, knows how far he can push.”

But when Obama announced his stimulus plan, none of the Republican proposals were included.

“The President said, you know, ‘Listen, elections have consequences and I won’ and he was going to get his way," Cantor said.

His efforts to work with Democrats had other consequences as well. A Tea Party backlash knocked Cantor from his Congressional seat in 2014.

Lots of Democrats don’t want Schumer to work with this president either.

Protestors have been gathering weekly outside his Brooklyn apartment, telling him to rally against Trump’s cabinet nominees. "We are the resistance and you work for us," they chanted outside Schumer's home.

Others are less worried about what the progressive wing of the party wants. Ten Democratic Senators can’t drift too far left because they are up for reelection next year in states that Trump won.

Cantor says Schumer has to consider both wings of the party when dealing with Trump.

“He’s going to have to weigh the risk of being an obstructionist and what that means in terms of the electoral outcomes in the midterms," he said.

But if cutting deals requires getting along, Trump isn’t trying that hard. He’s mocked Schumer for crying about the president’s executive order on immigration. He’s also called Schumer the Democrats’ “head clown” on Twitter.

Schumer says, sticks and stones.

“For about a month the president tried to flatter me — I’m his good friend," Schumer said recently. "Then he started calling names. None of them affect me. The bottom line is values. Our values as Democrats and Americans will affect whether I work with him or oppose him.”

Earlier this week, Schumer said he’s not sure Trump’s Supreme Court nominee meets that test. And both sides are a long way from throwing in the towel.