U.S.-China trade talks have hit another snag.

The next chapter in the saga involves the Trump administration considering cutting back on investments in China, a source familiar with the matter told CNBC on Friday. Stocks fell in response, with the Dow Jones Industrial Average shedding over 150 points.

Monday on CNBC, in the first on-the-record comment about such considerations, White House trade advisor Peter Navarro said the reports about them were "full of inaccuracies" and amounted to fake news.

If the White House were to go through with that move, "it would be an unmitigated disaster," says Stephen Roach, senior fellow at Yale University and former chairman of Morgan Stanley Asia.

"Open access to each other's markets [is] really important, especially with China likely to be the biggest consumer market in the world in the first half of this century," he told CNBC's "Trading Nation" on Friday.

Roach noted that the United States and China had been negotiating what's known as a "bilateral investment treaty" for about 10 years before the trade war began in an effort to open "our markets to China and China's markets to us."

"We got really close, but now it's been stalled out," Roach said. "We have bilateral investment treaties with 42 countries. China has them with 145. Free and open investment is the best way to enhance cross-border opportunities for multinational corporations, so we're going the wrong way. This really would concern me if we were to make progress on it."

Roach isn't the only one who's concerned. A University of Michigan survey released Friday revealed that near-record numbers of consumers cited trade policy as a negative factor stymieing U.S. economic progress.

And, when it comes down to it, the health of the U.S. consumer will be a major determinant in where the market goes next, Roach said.

"With the global economy really weakening, recession likely in Europe, downside in Japan and throughout east Asia, the American consumer has really been the only thing that's held the economy afloat," he said. "But with businesses in the U.S. turning cautious on capital spending, these are the same businesses that make decisions on hiring, and if they pull the plug on job growth, then consumers are in trouble."

In short, "there's not a lot of leeway should we get a soft patch," according to the Yale professor, and that's why U.S.-China trade talks stalling has Roach particularly concerned.

"This proposal [to pull U.S. investment] certainly doesn't make things any better," he said Friday. "The only progress that we have seen is in the so-called soybean strategy, where China could be counted on to buy more agricultural products, but the U.S., given its savings problem, has big trade deficits with over 100 countries right now, so there's no bilateral fix to our multilateral problem."

And the longer negotiators play hardball, the worse it's likely to get for both American workers and U.S. markets, Roach said.

"This'll do nothing [for] the American worker. It'll narrow the Chinese piece of our big trade deficit," he said of the "soybean strategy." "But the structural issues like technology transfer, intellectual property rights, state-owned enterprise subsidies? There's virtually no progress on any of those, and those are the big ones."

U.S. and Chinese trade officials are scheduled to resume talks on Oct. 10, sources told CNBC on Thursday.

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