Senate Majority Leader Mitch McConnell's failure to ram through an Obamacare repeal bill before the July 4 recess does more than reveal tribal divisions ravaging the Republican Party.

It also highlights President Donald Trump's role -- or lack of one -- in forging a GOP majority to squeeze the bill through the Senate, on an issue that has grave implications for the fate of the rest of his presidency.

Almost as soon as McConnell shelved a bid to vote on the measure this week, senators piled into a blue Capitol Police bus to head down to the White House for a brainstorming session with Trump.

The contrast was obvious to the euphoric Rose Garden rally that Trump hosted with GOP House members after they passed their Obamacare repeal bill in May. This time, Republicans sat around tables in the East Room expressing frustration at negative ads being aired against moderate Sen. Dean Heller, who has opposed the bill.

The delay in the Senate vote represents a failure -- that could yet be temporary -- by the GOP that has a monopoly on power in Washington yet can't yet honor the fundamental promise it has made to its voters for years.

But in this Washington cloud, there could be a silver lining for Trump.

A significant effort to reshape argument on the bill, to breach deep party divides on the issue and to sell a vision of health care reforms to Americans, could do a lot of good to a presidency that has been under siege for months.

It would also suggest that the President has a decent chance of building support for the rest of his agenda, that includes a push for tax reform and a program to repair the nation's decaying infrastructure.

JUST WATCHED Trump on health care: We're getting close Replay More Videos ... MUST WATCH Trump on health care: We're getting close 01:31

Can he do it?

But early signs are not encouraging for those who hope that the President can mine a golden seam of political support to get the bill passed.

Before grim-faced senators, the President spoke in vague terms about the bill, showing the lack of specificity that has hampered his attempts to wield political influence on Capitol Hill.

"We are going to try and solve the problem. So, I invited all of you. ... We are going to talk. We are going to see what we are going to do," Trump told the group, before offering an assessment that did not seem to reflect the aggravated state of Republican debate over the bill or address the specific concerns many senators have with the bill.

"We are getting very close," he said. "This will be great if we get it done," he said, before asking reporters to leave the room.

By now, everyone knows in Washington that the President is not keen on thrashing through the details of a bill to try to win wavering votes.

JUST WATCHED Kasich: Senate GOP health bill needs more funding Replay More Videos ... MUST WATCH Kasich: Senate GOP health bill needs more funding 06:20

In fact, he's often seemed ready to embrace any measure that he could portray as a political win -- whatever it contains.

There's certainly no sense that he is driving the debate toward an outcome that would fit into any ideological vision of his presidency. More often, he's shown more appetite to simply slam Obamacare than offer solutions.

Even Trump's supporters would admit that the President is yet to impose his considerable persona on Washington or shown he has the political skills and stock of capital to pilot legislation through Congress.

His consistency is also in question, since he labeled the House health care bill "mean," hanging members out to dry after celebrating its passage with them.

"Here's what I would tell any senator: If you're counting on the President to have your back, you need to watch it," GOP Sen. Lindsey Graham said Monday.

"This President is the first president in our history who has had neither political nor military experience," Maine Sen. Susan Collins told reporters on Capitol Hill Monday.

That impression will have to change if the President is to play on the loyalty of Republican senators who are against the bill, whom McConnell said used their White House meeting to explain their reservations to Trump.

Trump is the most unorthodox President in memory, and has broken many political norms. But if he is to amass a significant legislative legacy, he may have to put more political skin of his own in the game.

"He would knock peoples' socks off if he came forward with a venture of his own proposing," said Bruce Buchanan, a presidential historian at the University of Texas at Austin, who doubts Trump has such a play "in his playbook."

The next few weeks, as McConnell and Trump seek to unpick the GOP deadlock over the Senate proposal, pose a stern test for the President.

He must calm moderate senators scared about the consequences of voting for a measure the Congressional Budget Office says will lead to 22 million more people without coverage over the next decade.

Senate Republicans are also split on issues like cuts to the Medicaid expansion under Obamacare, the prospect of rising premiums for low income and working class Americans, and fears that opioid addicts could lose vital treatment.

Trump pushed back Wednesday morning against suggestions that he was not deeply involved in the process.

"Some of the Fake News Media likes to say that I am not totally engaged in healthcare. Wrong, I know the subject well & want victory for U.S.," he tweeted

JUST WATCHED Markey: GOP bill 'health care heartlessness' Replay More Videos ... MUST WATCH Markey: GOP bill 'health care heartlessness' 02:03

Can he unite Republicans?

Bringing Republicans together will test the clout of a president whose approval rating has dipped below 40% and has little support outside his, albeit solid, base. It will also reveal just how much loyalty Republican senators feel towards a President who has often departed from the orthodoxies of his own party.

Trump's stock on Capitol Hill may have taken a dent after a group that supports him, America First Policies, started airing ads against Heller in Nevada.

At the White House Tuesday, Heller and other senators complained, calling for party unity. Heller, a source said, brought the issue up first, while joking that he was disappointed that they used Matt Damon's face instead of his in the ad.

Trump may also need to up his persuasion game because though he's been speaking to holdout senators it's not clear he has changed many minds.

Utah Sen Mike Lee, a conservative who opposes the bill because he believes it does not do enough to strip down Obamacare, spoke to Trump by phone on Monday.

An aide said the tone of the call was "positive" but was also at a "high level" with no sign Trump addressed specific policy details.

McConnell said Tuesday that the President had been helpful and engaged. But he also appeared to hint that Trump would have to do more.

"We always anticipated the president would be very important in getting us to a conclusion. After all, under our system, he's the man with the signature," he said, adding that for Trump to show his cards earlier would have been a waste of time.

But Trump's time is now.

"There have been presidents that have been able to break through and Senate Majority leaders that have been able to put together a coalition," said Julian Zelizer, a CNN political analyst.

"(But) McConnell has been dealing with a President who has not been totally invested in this fight and is not selling to Americans what the idea is, behind the change other than people are going to lose many benefits."