(CNN) Donald Trump's self styling as the people's champion who would drain the Washington swamp got him to the White House.

But now that unique brand is in for a stern test as the President is battered by controversies over wealthy cabinet members living high on the taxpayer dime and as he pushes a tax plan that Democrats are already billing as a massive giveaway to Trump's rich friends.

Trump's transformation from a billionaire Manhattan real-estate magnate who jetted around in a private Boeing, into an advocate for the crushed dreams of middle class Americans in the globalized economy was one of the most audacious and successful aspects of his presidential campaign.

His outsider screeds lambasting a Beltway establishment steeped in political corruption were a perfect fit for a time when many voters thought their politicians were getting fat on government salaries and Washington perks and getting nothing done.

That's one reason why Health and Human Services Secretary Tom Price is now in deep trouble, amid a storm over his use of taxpayer dollars to finance flights on corporate jets -- even over short distances.

Trump left Price twisting in the wind on Wednesday.

"I will tell you personally, I'm not happy about it," Trump told reporters. "I'm going to look at it. I let him know it."

Asked if he would fire Price, the President replied: "We'll see."

Whether Price keeps his job in the end, Trump's comments were a clear sign that the President understands that the secretary's conduct, and that of several other members of the cabinet who took private jets, strikes at the heart of the drain the swamp narrative that he used to such effect last year.

And since Trump has made no attempt to broaden his support since taking office, the continued loyal support of his political base is an existential requirement for his presidency -- one reason why he has stoked cultural and race controversies that resonate with his largely white, rural constituency, including his showdown with kneeling NFL players.

But the shenanigans of cabinet members are not the only apparent contradiction with the roots of Trumpism that the President is going to have to square in the coming weeks.

The tax reform plan that Trump unveiled in Indiana on Wednesday is already being attacked as a typical Republican approach, that critics say would hand huge benefits to the rich -- i.e. people like the President himself.

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Selling the tax plan

With that in mind, Trump took care to frame the plan in terms that recalled the populist rhetoric of his campaign and the "American carnage" of shuttered factories and stolen jobs that he painted in his inaugural address.

"We're going to cut taxes for the middle class ... we are going to bring back the jobs and wealth that have left our country and most people thought left our country for good," Trump said.

"It's called a middle class miracle once again," he added. "It's also called a miracle for our great companies; a miracle for the middle class, for the working person."

The political problem here though is that Trump's description of the plan, his best hope of enacting a meaningful legislative reform before the mid-term elections next year, does not tell the whole story.

The proposals do call for a doubling of the standard deduction to $24,000 for married couples and $12,000 for single filers.

But the most sweeping overhaul of the tax system in generations also contains hefty giveaways for the wealthiest Americans, including in the abolition of the inheritance tax and proposes a cut in the corporate tax rate to 20%.

Trump argues this will lead to an explosion of economic growth that will create millions of jobs, and bring back firms from low wage economies overseas, and make everyone better off in a new era of highly charged growth.

But his approach has also offered a populist opening that Democrats will try to use in the months ahead to separate Trump from his electoral coalition, especially in the Midwest states that helped him secure victory last year.

"This is not tax reform - it's a thinly-veiled attempt to slash taxes for the wealthy while leaving the middle class, working families, and small business owners empty handed," said Democratic Rep. Joe Crowley of New York.

"This framework would also cause our national debt to spike, resulting in Republican leaders cutting even more from critical programs that help American families, like Social Security, Medicare, and Medicaid, to offset the massive tax cuts they've gifted to the rich," he added.

Trump quickly tried to dispel the notion that he would personally benefit from his own changes to the tax system.

"It's not good for me, believe me," Trump said.

Democrats are certain to use that omission to try again to pressure the President to reveal how much tax he pays -- though their efforts to damage him on the issue during the campaign foundered to their intense frustration.

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Fighting for the middle class vote

Last year, according to exit polls, Trump succeeded in convincing voters that he would take care of the middle class better than Hillary Clinton would.

He narrowly won voters earning between $50,000 and $200,000 a year, who make up more than half of the total electorate. Attacks on the President's secrecy about his wealth looked promising for Democrats ahead of the general election campaign, but failed to disqualify Trump.

The question now is whether the unshakable connection with the middle class voters in Trump's base will remain rock solid as takes steps to change America that affect the money in everyone's wallets and as Washington controversies suggest members of his cabinet are hypocrites.

One reason why it might is that Trump's compact with his base voters is as much emotional, and tonal, as achieved by nitty gritty policy details that can be found in budgets and tax plans.

No candidate in years had grasped or voiced the economic grievances of people who did not recognize the economic progress wrought after the Great Recession that Democrats touted during the campaign.

While his Boeing had gold-plated seat belts, Trump was sometimes pictured sitting on it while munching a burger from a fast food chain while his earthy diction and politically incorrect stump speeches positioned him as a man of unsophisticated, and certainly not elite, tastes.

At the same time, Trump's tirades against trade deals with nations like China p layed into a belief among many people that such pacts had hollowed out the American dream, while building middle classes lives for citizens of adversary nations.

While some of his populist, nationalist advisers, like Steve Bannon, have now left his side, the President has been careful to highlight his suspicion of free trade pacts, ordering a renegotiation of NAFTA and a slamming a deal with US ally South Korea -- even amidst a nuclear showdown with the North.

That's all in the service of maintaining his connection to the voters that sent him to the Oval Office.