Compared with polling from when Trump took office, perceptions of the president’s performance have plummeted on the federal budget deficit, on improving the health-care system and on the economy.

Perhaps the greatest danger to Trump’s political future is the cost of these negative perceptions to his brand. The president was elected, in part, by giving his supporters an impression of business acumen. This was, in fact, the image carefully cultivated by book publishers and TV producers. And by Trump himself as a presidential candidate, who claimed to be a peerless negotiator, an unrivaled businessman and an excellent manager.

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These claims can now be believed only by the ideologically addled.

The problem for Trump is not only that he lost the most visible and important confrontation of his presidency — in negotiating with House Speaker Nancy Pelosi (D-Calif.) over the government shutdown. It is that his methods are so blunt and transparent. His typical tactic is to raise the stakes of a negotiation impossibly high — a government shutdown or nuclear war — then to make a maximal demand and trust in the triumph of his stronger will. It is a form of negotiation ended by someone saying “uncle.” That Trump ended up in abject humiliation was perhaps fated by biology: You can angrily hold your breath for only so long.

If, in the next stage, the loser acts unilaterally under the pretense of a border security crisis, it will merely prove that Trump is a dangerously sore loser. For the MBAs taking notes, this complex negotiating strategy is known as: Throwing the game off the table if you can’t win.

Meanwhile, in a variety of global negotiations, American opponents need only master one method: flattery. In Trump’s words, “I know people, because deals are people. . . . If [Russian President Vladimir] Putin respects me, and if Putin wants to call me brilliant, and other things that he said which were, frankly, very nice, I’ll accept that.” Taken at face value, Trump is arguing: Deals are people. People who praise me have good judgment. Thus, people who praise me make good deals. Hearing these sentiments from an American president is enough to gag a historian. It is pathetic gullibility elevated into the realm of theory. It should concern us that the American president is a source of global derision and national shame.

The other branding claims made by Trump have become equally incredible. His reputation as a self-made billionaire lies in ruins. An extensive New York Times article on Trump’s wealth found a bassinet millionaire, consistently bailed out of bad bets, who dodged gift taxes, milked his empire for cash and cultivated a deceptive image of business brilliance. And special counsel Robert S. Mueller III’s investigation may reveal serious corruption and perjury in cataloguing Trump’s 30-year panting desire to sell his brand in Russia.

And who can take Trump seriously as a manager? He has a talent for weeding out the talented and responsible. He is a world-class nepotist. He is incapable of delegation or of taking conflicting advice. He is unreliable in dealing with his allies. He is capable of taking several conflicting policy views on the same topic — be it health care, or the “dreamers,” or gun control — in a matter of days or hours. He often has no clear goals. He has no attention span and is consistently ignorant of details. He is prone to vicious and public abuse of rivals and of employees. Try to put that profile up on LinkedIn.

Those 37 percent who approve of Trump’s performance may point to the state of the economy or the composition of the Supreme Court. They may be impressed by his destruction of norms or enthused by his promotion of exclusion. They may want a president who speaks his mind, even when it is hateful gibberish. They may want a president who is an institutional arsonist, even if the result is mere destruction.

But no one can reasonably claim to believe in Trump’s brand as it was sold in 2016. We have plumbed the shallows of his boasts. They are refuted lies. And whatever else the president may be, he is a fraud.