This story is an updated version of a report CNNPolitics.com published last month . It has been updated to reflect recent developments.

(CNN) A few hours after the House finally passed a bill to repeal and replace the Affordable Care Act last month, Senate Majority Leader Mitch McConnell walked silently and expressionless from his office to a waiting black SUV outside the Capitol. Only his police detail and an aide were with him as he left the quiet building and drove off.

The solitary scene was a sharp contrast from the crowded and boisterous victory rally President Donald Trump threw for relieved House Republicans that same day in the White House Rose Garden after the vote. But it may capture the low-key, no-frills style of McConnell, the determined Senate majority leader from Kentucky, that could serve him well as he takes on one of the most important legislative challenges of his career.

All eyes are now on McConnell and his fellow Senate Republicans to see if they can accomplish what the House GOP did through fits and starts: Pull together an ideologically diverse conference and secure enough votes to get rid of Obamacare, a promise they've made repeatedly but failed to keep since President Barack Obama's health care law passed in 2010.

"The Senate is looking forward to getting it," Trump said after the House vote. "Mitch McConnell knows how to do things, and I think we're going to have some really great health care for a long time."

As of Monday, Senate GOP leaders had released their latest version of their health care legislation, which includes a provision meant to incentivize individuals to maintain their health insurance coverage regardless of whether they are sick. So far, at least five Republicans have said they oppose the legislation as written . McConnell can only lose two and still pass the bill, and he's set the deadline of passing the bill by the end of this week.

McConnell, who has led the Senate Republicans for a decade, may be one of the most disciplined politicians in America and therefore uniquely suited for the task. He will need all the self-control and detachment he can muster to steer the complex health bill through the competing demands -- and passions -- of the various factions of his caucus while also writing effective legislation that could set the nation's health policy for a generation.

McConnell's reputation is that of the ultimate Washington insider, a talented legislative tactician who utilizes the dense Senate rules to achieve his goals. Those skills will be on display as he works to maximize what can pass using the Senate's complicated budget reconciliation process, which will allow Republicans to pass a repeal without any Democratic votes.

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His working knowledge of the specialized ways of Washington, gained through 30 years in the Senate, make him someone who Trump, the outsider, needs to lean on to get the Obamacare repeal and other legislation passed. To date, despite GOP control of both chambers of Congress and the White House, Republicans have yet to score any major legislative accomplishments. That adds pressure on McConnell to get health care across the finish line.

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A politician who doesn't seek the limelight

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McConnell is accustomed to the limelight even if he doesn't seek to bathe in it the way many politicians do. The 75-year-old sixth-term Kentuckian was unflinching in the face of withering criticism from Democrats after he blocked Merrick Garland , President Barack Obama's nominee to the Supreme Court, last year and then used the "nuclear option" to make it easier for Trump to put his nominee, Neil Gorsuch , on the court. His defiance and fortitude won him praise and loyalty from most Republicans -- including Trump.

Republican senators routinely praise McConnell's leadership skills and soft-spoken but direct messaging style. For the most part, he doesn't suffer from the damaging internal backbiting many legislative leaders encounter. Texas GOP Sen. Ted Cruz once called him a "liar" on the Senate floor, but the clash was an aberration and McConnell responded coolly, dispatching other senior senators to chastise the younger Cruz.

The only time recently that McConnell has shown anger in public was during a February debate over the nomination of then-Sen. Jeff Sessions, R-Alabama, to be attorney general, when McConnell abruptly interrupted Sen. Elizabeth Warren and accused her of breaking Senate rules that forbid one senator from disparaging another member on the floor, something she denied doing.

"She was warned. She was given an explanation. Nevertheless, she persisted," McConnell said of Warren.

In the end, the late-night dust-up probably bolstered Warren's standing with liberals more than anything else.

Annoyance can he heard in McConnell's voice occasionally on the floor when he gets into a back-and-forth with Democratic Leader Chuck Schumer, D-New York, just as it could in his dealings with Schumer's predecessor, Harry Reid of Nevada. But McConnell is typically on-message, reading dryly from a well-honed text written by his staff that lays out exactly what he wants to say about a given issue, and not an ounce more or less.

And McConnell doesn't mind hammering his messages home, often repeating the same lines day after day until they take root in the debate.

At news conferences, McConnell is unflappable, deflecting reporters who regularly bait him to criticize Trump. McConnell will be straightforward when he disagrees with the President -- and has said he should stop tweeting so much -- but McConnell has yet to make a major gaffe as he has juggled countless questions about Trump's unorthodox presidency.

While McConnell is from the establishment wing of the party, he got behind Trump once the businessman won the nomination and never wavered the way House Speaker Paul Ryan did. While the two men are not close friends, they have a respectful working relationship. They meet in person or speak on the phone regularly. Trump called McConnell after the House vote in May, according to a White House official, to deliver the message that it's now the Senate leader's task to complete the work.

McConnell is tighter with Vice President Mike Pence, the former House member who attends weekly meetings with Senate Republicans, and who was a critical force in getting the repeal bill through the House. Pence is expected to play a similar role as the Senate considers the bill.

Quiet persuasion may be key to success

For all his strengths as a politician, what McConnell may need most is the power of quiet persuasion as he works private meetings and phone calls to convince conservative Republicans like Cruz and Sens. Mike Lee of Utah and Ron Johnson of Wisconsin to accept an outcome that more moderate members of the caucus like Susan Collins of Maine and Lisa Murkowski of Alaska could vote for too.

He might also need the courage to cut loose someone like Collins -- or fellow Kentuckian Sen. Rand Paul, who has blasted the House bill -- if he feels they won't support an emerging deal, something GOP aides say could happen.

McConnell can afford to lose two members of his caucus and still get 51 votes with a tie-breaking vote from Pence.

McConnell led a 13-member Senate working group on health care that went behind closed-doors to hammer out a compromise over the past several weeks.

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If the deal they reached can pass the Senate, McConnell then must determine whether to go into negotiations with the House to resolve differences between their bills or just send the House the Senate bill and force it to "take-it-or-leave it." McConnell's decision would be critical because, while the pressure could be enormous on the House to accept whatever the Senate can pass, it would be a risky gambit in that House Republicans could reject the Senate bill and the whole effort could fail.

Each Republican senator has unique policy and political needs related the bill. It's McConnell's job to understand and respect each situation and continue to tinker with the final bill. He then must persuade the others, especially those not thrilled with the final agreement, to support it anyway.