Herman Cain certainly has an issue. He’s put all his chips on 9-9-9 and brazenly dismissed critics as know-nothings or misrepresenters of his plan. It’s become obvious, however, that it is he who is trying to pull a fast on. First Read discovers what many of us have: The plan is highly regressive. Yet another independent set of eyes has looked at Cain’s plan now:

The nonpartisan Tax Policy Center is readying a report on Cain’s plan, though it is waiting for more details from the campaign. But it has come to some conclusions already.

Cain’s plan “cuts taxes for the rich and raises taxes on the poor,” Roberton Williams, a senior fellow at the center, tells First Read. He added that it would create a “much more regressive tax system.”

The plan would represent a “major tax cut” for the rich and raise taxes “substantially” on the poor and middle class, Williams said. “Given that a big chunk doesn’t pay any income tax, this would be a big tax increase on people at bottom end. At the top end, the opposite happens.”

The top end would go from about a 35% income tax rate to 9%. “That’s a big, big drop,” Williams said, adding that the capital-gains tax would be another added benefit for the wealthiest. “People at the top would see far and away the largest share of the gains. Those people are going to see a huge tax cut.”

Moreover, Cain’s habit of refusing to admit error is becoming a liability:

“Today under the current system, [a family making $50,000 a year is] will pay over $10,000 in taxes, assuming standard deductions and standard exemptions,” Cain claimed. “I’ve gone through the math — $10,000. Now, with 9-9-9, they’re going to pay that 9% personal tax on their income, so that’s only $4,500. They still have $5,500 left over to apply to the sales tax piece, and if you go and look at how much of it they would probably spend on sales taxes for new goods, not used, used goods they don’t pay a sales tax. They are still going to have money left over, Chuck.”

But that is not exactly the case.

In fact, a family making $50,000 a year with two children would only pay about $776 in income taxes when standard deductions are factored in, based on 2010 Internal Revenue Service levels. (In fact, not factoring in deductions, a married couple filing jointly making $50,000 a year would pay $6,666 in income tax, not $10,000. But what’s important for tax purposes is “taxable” income.)

ABC News has also found that Cain’s plan doubles the tax burden on the middle class. Cain may not have been aware of the regressive nature of his plan. Perhaps he doesn’t care about progressivity, as his tax thinker Rich Lowrie told me the other day.

In either case, it’s painfully clear that Cain’s plan and the adviser who came up with it have glaring flaws. The more Cain persists in denying factual matters, the more this becomes not only a policy problem but a character problem. Is this how he would govern? Is he someone who can learn from mistakes? Will he refuse to listen to valid criticism? Does he know what he is doing?

Moreover, there is new criticism of his sales tax from the conservative base, whose support is essential to his winning early primary states. Gary Bauer, among the most prominent of Christian conservatives and a former presidential candidate himself, writes in his daily e-mail (sent to a huge conservative audience): “Rick Santorum and Michele Bachmann both pointed out the most obvious concern many have with Cain’s plan: It gives the government another revenue stream. While many conservatives like the idea of a national sales tax, they want it to replace the income tax. While Cain is calling for a radically reduced tax structure, it is undeniable that he is also calling for a new tax on top of the income tax. Moreover, seniors and retirees on fixed incomes are not too keen about paying a new tax on food and medicine either.” If that sentiment is widespread among evangelical voters and/or retirees (who are prominent in Iowa), Cain will be in trouble.

Finally, Cain’s plan has one more wrinkle. Used goods are exempt from the 9 percent sales tax. That doesn’t do much for the poor who aren’t buying used bread. Moreover, it raises a massive enforcement problem. How many car dealerships will become “lightly used” dealerships (let an employee take it home for the weekend first)? Remember that Cain isn’t getting rid of the income tax so the IRS will remain. Indeed, the feds will have to add a legion of agents to call foul on millions of faux used transactions.

Here’s a simple suggestion for Cain: In the next debate, explain that 9-9-9 was meant to start a robust discussion about tax reform. It’s open to review and refinement. He should announce a new team of advisers, including some of the economists who have criticized the plan.When he gets elected, he should explain, the finalized plan will not be regressive, but it will be pro-growth. And he should promise to look again at the introduction of a new revenue stream for the federal government.

Sure, that’s going to be sort of embarrassing. But the alternative is to deny reality and lose credibility with voters. We already have a president who’s made that mistake.