WASHINGTON >> When Rep. Nancy Pelosi, the House Democratic leader, introduced Sen. Chuck Schumer, D-N.Y., to members of her caucus earlier this month, she warmed up the room with a well-worn joke about her Senate counterpart: “You know they say the most dangerous place in Washington is between Chuck and a camera.”

Schumer’s love of the spotlight aside, it has been behind the scenes where “Chuck and Nancy,” as President Donald Trump calls them, have forged what may be the most surprisingly potent partnership in Trump’s Washington.

In a city where they hold no formal reins of power, the two are helping to set the agenda on Capitol Hill. They cut a fiscal deal with Trump, then reached a tentative agreement to protect young immigrants in the country illegally from deportation.

Now they face a tougher test: Killing the latest Republican effort to repeal the Affordable Care Act, and persuading the mercurial president to work with them to shore up shaky health insurance markets.

“This bill is really a stinkeroo,” Pelosi said today, referring to the repeal measure drafted by Sens. Lindsey Graham of South Carolina and Bill Cassidy of Louisiana. “I hope that when this is defeated, and hopefully that will be soon, the president will agree to going forward in a bipartisan way.”

It will not be easy. Trump is pressing Congress to adopt the health care legislation, which would cut deeply into Medicaid and dismantle the programs and prescriptions of the Affordable Care Act.

But if the bill can be stopped, the Democratic leaders have already begun nudging the president toward another about-face: setting aside the mantra of “repeal and replace” and adopting modest measures to make his predecessor’s signature domestic achievement work better.

During a recent White House dinner, the pair pushed Trump to make permanent the subsidies, known as cost-sharing reductions, paid to insurers under the health law to help low-income customers pay for out-of-pocket health expenses like co-payments and deductibles. Trump has threatened to end such payments, raising uncertainty in insurance markets and boosting premiums.

In separate interviews, both leaders said that the president was noncommittal, and that their future dealings with him would depend on whether he followed through on his pledge to protect young unauthorized immigrants brought here as children — beneficiaries of the Obama-era program Trump is winding down known as Deferred Action for Childhood Arrivals, or DACA.

“Whether he pivots or not will be one of the most fundamental questions of this administration,” Schumer said. “It’s the $64,000 question. The only way it can happen is if we have a successful negotiation on DACA, and secondly whether we get health care.”

In some respects, Pelosi and Schumer are an unlikely pair. She represents San Francisco, and for years has been the subject of harsh attacks from Republicans, who caricature her as affluent, elitist and permissive. He is from Brooklyn and far more attuned to the needs of big business and Wall Street. She is button-down and always on message — at least in public. (In private, she calls Schumer “Chuckles.”) He is more freewheeling and off the cuff.

When she was House speaker, her real Senate partner was the then-majority leader, Harry Reid, with whom she helped pass some of the biggest legislative achievements of a generation: the Affordable Care Act, the Dodd-Frank Wall Street regulatory law, the 2009 economic stimulus and President George W. Bush’s Wall Street rescue.

But Pelosi’s former chief of staff, John Lawrence, said what while she and Reid worked well together, “I don’t have the sense it was the same instinctual harmonic relationship that she has with Chuck.”

Pelosi said she and Schumer know one another so well that “we speak in shorthand to each other.”

Pelosi said she and Schumer were still assessing whether they could trust Trump. “We will trust each other as long as we can,” she said, adding, “It’s one issue at a time.”

Meanwhile, some Democrats are watching with a skeptical eye.

“I hope and pray that Pelosi and Schumer are more sophisticated and smarter than everyone else that’s been duped by Donald Trump,” said Rep. Luis V. Gutiérrez, D-Ill., after the Democratic leaders announced their tentative deal with Trump to pursue legislation allowing the young immigrants to stay in the United States.

Others see cause for optimism. Several Democratic senators, including Heidi Heitkamp of North Dakota and Richard Blumenthal of Connecticut, said they could foresee Pelosi and Schumer reaching an agreement with Trump on legislation to repair the nation’s crumbling infrastructure, an interest of all three of them.

In working with a president so despised by Democratic voters, especially those on the far left, the two Democrats must tread carefully. Pelosi got a taste of that this week in San Francisco, when she was shouted down by protesters during a news conference where she had intended to talk about the DREAM Act, legislation to offer legal status and a path to citizenship for young, unauthorized immigrants brought to the United States as children.

But some Democratic strategists say the leaders have little to lose.

“I think they are in position to make deals that are good for Democratic priorities and that have the support of the Democratic caucus,” said Geoff Garin, Schumer’s pollster. “And if the deals don’t do those things, then it’s easy for them to walk away.”

Pelosi and Schumer were both traveling with their families on separate vacations in Italy this summer when, each said, they began to strategize on how to use a looming fight over the debt ceiling as leverage to negotiate with Trump. Schumer said he proposed urging the White House to extend the debt ceiling for three months, which would force a vote again in December, giving the Democrats leverage over other agenda items. Pelosi, he said, quickly agreed.

“We were in sync,” Pelosi said. The debt ceiling deal opened the door to the dinner, where the two leaders raised the issue of DACA immigrants. Pelosi said it was important for the president to hear that Schumer — who became minority leader just this year — was as committed to their fate as she was.

“That’s the beauty of it,” she said. “I’m the usual suspect, and he’s the new leader coming in.”

The Pelosi-Schumer relationship dates to 1987, when Pelosi, a former chairwoman of the California Democratic Party, was a newly elected congresswoman. Her fellow Californian, Rep. George Miller — who was then Schumer’s landlord and roommate — invited her to a dinner at an Italian restaurant near the Capitol. A collection of House members, including Schumer, gathered there each Tuesday night to bat around policy ideas.

Miller gave Pelosi an auspicious introduction: “You’re going to meet Nancy Pelosi,” Schumer recalls him saying. “She’s going to become the first woman speaker.”

Miller was proved correct 20 years later.

“The relationship is longtime,” said Miller, who retired from the House in 2015. “They’ve had their spats, they’ve had their agreements, they’ve had their strategies become successful and they’ve had their strategies fall flat on their face, and that’s why this is working.”

They have not always seen eye to eye. In 2014, Pelosi publicly criticized Schumer when he said it was a tactical mistake for Democrats to have put a health care overhaul on the top of their agenda in 2009 after Barack Obama was elected president. Many analysts believe public anger over the Affordable Care Act cost Democrats control of the House in 2010.

“We come here to do a job, not keep a job,” Pelosi said then. In a reference to those who gained insurance under the bill, she added, “There are more than 14 million reasons why that’s wrong.”