President Donald Trump, flanked by Senate Majority Leader Mitch McConnell of Ky., left, and House Speaker Paul Ryan of Wis., speaks during a meeting with House and Senate leadership, Wednesday, March 1, 2017 at the White House in Washington. (Evan Vucci/AP)

President Trump’s administration was still in its first hours when Mitch McConnell snagged an open seat next to him for a private chat at his inaugural luncheon. For more than 15 minutes, McConnell did most of the talking. The new president listened keenly.

Eleven days later, McConnell had a front-row seat as Trump announced Neil M. Gorsuch as his pick for the Supreme Court, the culmination of the Senate majority leader’s advice during the campaign on how to handle the court vacancy: Consult the Federalist Society, and make a list of prospects. Trump did that.

For months, McConnell, the consummate political insider, has been dispensing his counsel to Trump, the ultimate outsider, who has been absorbing the Kentuckian’s words. The dynamic has provided a degree of stability in the still-forming relationship between the low-key Senate leader and the loquacious president, who are starkly different types of people.

But cracks have also emerged in their partnership, most notably when Trump has casually suggested that McConnell change the long-standing rules of the Senate and McConnell has bluntly brushed him off.

Their fragile alliance is about to face its biggest challenge yet in the next phase of the Republican effort to overhaul the nation’s health-care laws. The work of revising major parts of the act known as Obamacare is now in the Senate’s hands after the House narrowly passed its own bill following months of destructive Republican infighting.

Trump, then the president-elect, walks through the Capitol Building with his wife Melania, left, Nov. 10 after meeting with McConnell, right. (Bill O'Leary/The Washington Post)

At stake is the long-term future of the American health-care system and the near-term future of the new Republican-controlled government — which has yet to shepherd any major legislative proposals into law.

“Whether or not they are able to forge a positive, personal and working relationship will be one of the early tests of this,” said former Republican National Committee chairman Michael Steele.

[Health care is now set to be a defining issue in the next election cycles]

It will be as much a make-or-break moment for McConnell as for Trump. The Senate leader has so far been able to fly below the radar on health care as House Republicans worked through their disagreements before ultimately passing a bill. If he cannot do the same, he is likely to be blamed for the collapse of the effort to fulfill a signature GOP campaign promise.

McConnell is cool and deliberative while Trump is hot and impetuous. But they have privately developed what people close to them say is a respectful relationship.

In the 75-year-old majority leader, Trump, 70, sees a senior player in navigating the ways of Washington, in both age and experience. He views him as someone on his level — or at least more on his level than many other Republicans, including House Speaker Paul D. Ryan (R-Wis.).

In some regards, McConnell has become a tutor to Trump. The two men speak regularly, with McConnell initiating some calls to guide the novice president.

(Jenny Starrs/The Washington Post)

“Leader McConnell has been a great resource in giving guidance and counsel on a myriad of issues in the first few months,” said one senior administration official — talking generically about McConnell — who spoke on the condition of anonymity to discuss the relationship candidly.

It was McConnell, after all, who helped hand Trump his only major congressional victory during his first 100 days in office: the confirmation of Gorsuch to the high court. In nominating Gorsuch, who won wide praise in conservative circles, Trump also aided McConnell by helping him pay off his gamble to hold the seat open during the presidential campaign.

Those close to McConnell say that his relationship with Trump is rooted in trying to accomplish the things Republicans campaigned on last year — no more, no less.

“The funny thing — everybody used to ask McConnell if he got along with Barack Obama,” said Josh Holmes, McConnell’s former chief of staff. “And he said it’s irrelevant if he got along. It’s, ‘Can we work together?’ ”

But Holmes said McConnell is “allergic to drama” and “does not see the business of governing as a soap opera. It’s a business that should be handled professionally.” That ideal has been complicated time and again by Trump’s controversial policies and pronouncements.

That is one area where McConnell’s private lobbying has made little difference. In an interview with The Washington Post earlier this year, McConnell made it clear that he was not a fan of Trump’s hostile Twitter habits. He said that he liked what Trump was doing a lot more than what he was writing on social media.

“We’ve had very candid conversations about that. And as you can see, my advice has not made a bit of difference,” McConnell said.

[The Take: Can the GOP sell its health-care proposal to a skeptical public?]

The health-care debate in the Senate is expected be a more-complicated endeavor than Gorsuch’s confirmation or the short-term government-spending deal the White House recently reached with Congress. It will test McConnell’s ability to influence Trump behind the scenes as never before.

McConnell aides and allies are hoping that the White House will let the Senate work through its differences on health care without setting artificial deadlines or trying to hurry the process ahead.

“We’re not going to rush it,” said Sen. John Thune (R-S.D.), one of McConnell’s top lieutenants.

Senate Republicans have shown little regard for the controversial House bill, signaling that they are going to write their own measure. A working group of 13 GOP senators from different parts of the ideological spectrum is meeting twice a week to talk about how to move ahead.

“The Senate is the place, still, in my view, where you deliberate, you have a say, you vote,” said Sen. Lindsey O. Graham (R-S.C.).

The Trump administration has been working with the Senate and House along “dual tracks” on health care, according to the senior administration official. McConnell aides and allies said that they expected the president’s team to be heavily involved in the process moving forward.

But part of McConnell’s challenge will be convincing Trump that the methodical pace at which the Senate moves is necessary.

“Here [in Congress], it’s just the slow pace that is very hard for anyone coming out of the private sector as a CEO to become comfortable with,” said Rep. Chris Collins (R-N.Y.) a Trump ally, in a recent interview.

But some of the long-standing Senate norms and customs to which McConnell claims to be committed have been shrugged off by Trump as mere inconveniences in the lawmaking process. Trump suggested Tuesday on Twitter that it might be time to do away with the 60-vote Senate threshold on legislation, which empowers the minority party.

“We’re not going to do that,” McConnell said dismissively later that day, arguing that “it would fundamentally change the way the Senate has worked for a very long time.”

Even as the relationship between McConnell and Trump has seen its share of tensions, it has generally been better than Trump’s relationship with Ryan, who wavered in his support of Trump during the campaign.

McConnell was never Trump’s biggest cheerleader in 2016, but he supported him and generally kept his criticism narrowly focused on words Trump spoke or actions he took that bothered him.

[Republicans’ health-care plan could launch some ugly political battles in state legislatures]

That small measure of loyalty in the trenches has been remembered in the West Wing. McConnell, unlike Ryan, has not been saddled with a reputation as a fair-weather friend.

“McConnell never took his eye off the ball and lost sight of the fact that at the end of the day, no matter what individual issue was happening, it was going to be Trump or [Democratic nominee Hillary] Clinton,” said Scott Jennings, a former McConnell strategist, noting that he “far preferred Trump.”

Even in Trump’s administration, which is filled with political newcomers, the reach of McConnell’s vast network of former staffers and allies from more than 32 years in the Senate can be felt. McConnell’s wife, Elaine Chao, is Trump’s transportation secretary. Amy Swonger, Trump’s head of the Senate legislative affairs team, is a former McConnell aide. So is Andrew Bremberg, director of the Domestic Policy Council.

On the whole, though, Trump’s team is largely bereft of experienced Senate tacticians. In addition to dealing with Trump, McConnell deals mainly with Chief of Staff Reince Priebus, budget director Mick Mulvaney and Vice President Pence, according to a person familiar with the situation.

For Trump, the health-care debate in the Senate will not only depend on how well he can work with McConnell. It is also likely to rest on his interaction with rank-and-file Republican senators.

As the House was working on its health-care bill, Trump held meetings with centrist and conservative GOP members as he sought to build support for the measure. But some McConnell allies doubt that kind of courtship will work as well in the Senate.

“I’m not sure that U.S. senators that have been in office for a long time and have their own opinions and ideas on legislation need some hand-holding from outside entities,” said Jennings, the former McConnell strategist. In the House, he added, “maybe they needed a little more prodding and guiding.”