The World Trade Organization said uncertainty about a possible trade war is already dragging down the world economy. The WTO issued the warning just before new U.S. tariffs on $34 billion of Chinese imports go into effect at midnight Thursday. China said it will not "fire the first shot," but will impose tariffs on American goods immediately if the U.S. follows through.

But according to Eurasia Group president and CBS News contributor Ian Bremmer, "It won't have that much impact."

"We are going to see in almost all likelihood tariffs on some $34 billion of goods come down from the United States on China on Friday. And certainly within just a few hours, the Chinese, when that happens, will come back against the United States and then we'll take a collective breath. It won't have that much impact. They'll be forgotten about within sort of a day I would say in terms of the markets themselves, and then we'll see, are they going to start engaging," Bremmer said Thursday on "CBS This Morning."

Bremmer said both the U.S. and China have been backing down on former threats about a possible trade war.

"Like for example, we were talking about making it much more difficult for the Chinese to invest into the United States in technology. Trump backed off a couple weeks ago on implementing what would have been significant measures against them. You're familiar with the Chinese telecom firm ZTE. They were going to be made bankrupt by White House regulations what were being put in place. Trump himself intervened with a tweet saying, we don't want to lose all of those Chinese jobs," Bremmer said. "So actually, Trump as you know respects the strongman. He's had better relationships personally with people like Putin, Kim Jong Un, Xi Jinping – remember that Mar-a-Lago summer, by far the best of his first year – than he has with many of his own allies."

Bremmer said Mr. Trump knows China can be problematic when it comes to trade – "market access reciprocity, stealing intellectual property."

"But he also knows that China can hit back really hard and they can hit back in a targeted way against red states, against American farmers. So I would be very surprised if we saw significant escalation as opposed to significant rhetoric before elections in the U.S. in November, which is what we're really talking about here."

Bremmer said he has spoken with American CEOs who were happy with the Trump administration's first year in regard to things like tax cuts and regulatory rollbacks, but they wondered if Mr. Trump knew "what he's talking about" when it came to tariffs and trade deficits.

"I've had American CEOs come to me and say, 'When he talks about the deficit, is that just for politics? Or does he really believe that that's what drives America being advantaged or not as an economy?' And when you say, 'No, he really does focus on that,' they kind of don't believe it, right? Because it's not the way business works," Bremmer said. "So certainly the fact that we're now talking about automotive tariffs against the Europeans – where there is a problem, where the European tariffs against U.S. cars are four times what the American tariffs are against European cars – that's something that potentially really disrupts supply chain and will hurt American corporations and eventually the American economy."

