President Trump has moved his push for tax reform to a new phase: He's trying to convince blue collar and lower middle class America that tax cuts for big corporations will put more money in their pockets too.

It's a tall order.

It began Wednesday night at a rally in Pennsylvania where he made a bold claim about how his plan for major corporate tax relief would help middle class families:

We will totally eliminate the penalty on returning future earnings back to the United States and we will impose a one-time low tax on money currently parked overseas so it can be brought back home to America, where it belongs and where it can do its job. My counsel of economic advisers estimates that this change, along with a lower tax rate, would likely give the typical American household a $4,000 pay raise.

Raise your hand if you thought the title of "Billionaire populist barnstorming campaigner for trickle down economics" wasn't possible before now.

But that's what President Trump has essentially become. For the first time since the Reagan era, a president is furiously pushing the idea that giving tax breaks to super rich corporations is the key to unleashing economic gains for everyone else down the economic ladder.

Sure, "trickle down" and "voodoo economics" were terms President Reagan's critics created to denigrate his ideas. But President Kennedy made similar arguments beginning in 1962 pushing for his tax cut plan that President Johnson eventually got enacted in 1964.

Trump is going even further than Reagan or Kennedy to press for tax cuts, barnstorming the country with recent stops in North Dakota, Indiana, Missouri, and now Pennsylvania.

The truth is, the plan needs this kind of extraordinary campaign-style effort. A new Reuters/Ipsos poll released just as President Trump was on his way to Pennsylvania shows that most Americans are more focused on getting the rich to pay more in taxes. The survey found 53 percent of adults "strongly agree" and 23 percent "somewhat agree" that the wealthiest Americans should pay higher tax rates.

Trump needs to convince a good segment of those people and their representatives of at least two things. First, that corporations are not the same as "the rich." And second, that cutting corporate taxes is a good way to get the middle class an economic boost.

It won't be easy.

There is evidence some parts of the Trump plan would specifically help middle class taxpayers. The proposal to double the standard deduction for the nearly 80 percent of filers who don't itemize their taxes is the best example of that. But more should be done. Most importantly, the president must restore all the tax deductions for the middle class eliminated in the plan that dilute the positive effects of the doubling of the standard deduction. Keeping state and local tax deductions would be a good place to start.

Doing these things might work as well as speeches to convince wary Republicans and maybe even some Democrats to support the bill.

President Trump is clearly more invigorated and personally invested in tax reform than he was with health care, which may have undermined that cause. It isn't just the speeches across the country, but the deft moves of gathering truckers Wednesday night's rally and making sure Democrats like Senators Heidi Heitkamp and Joe Donnelly showed up at his tax reform speeches in North Dakota and Indiana, respectively.

But it's going to take added strategies to overcome an American public that is clearly wary of anything that could help the rich. And the fact is, meaningfully cutting taxes will almost always benefit the rich the most. There will likely continue to be daily news reports and studies showing how the rich will gain significantly from the Trump plan. In this environment, it's obvious why so many of the president's Republican predecessors and GOP members of Congress avoided taking on this challenge. But apparently, this is more attractive to the ever-combative President Trump.

This tax fight will surely test just how effective he really is. But beyond repeating his current message in more cities, Trump is going to need to change the headlines by doing more to help ordinary working people.

The job of doing that has just begun.

Commentary by Jake Novak, CNBC.com senior columnist. Follow him on Twitter @jakejakeny.

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