New York (CNN Business) The trade war is doing real damage to the American economy, and it's showing up in manufacturing. Factories in a wide range of businesses, from clothing to machinery are suffering declines in exports.

The slowdown in manufacturing — often an early indicator of problems in the wider economy — showed up starkly in a dreadful report released on Tuesday. Factory activity contracted in September for the second straight month; by some measures it was the worst month in a decade. The bad news spooked investors and the Dow fell nearly 350 points, or 1.3%.

We have now tariffed our way into a manufacturing recession in the US and globally."

President Donald Trump wasted little time finding someone to blame for the gloomy factory activity.

"As I predicted, Jay Powell and the Federal Reserve have allowed the Dollar to get so strong, especially relative to ALL other currencies, that our manufacturers are being negatively affected," Trump tweeted minutes after the report was released.

The president continued to blast his handpicked Fed chief, calling the central bank "pathetic."

Trump's blame-the-Fed narrative is not supported by the evidence.

The Institute for Supply Management's manufacturing report did not mention Fed policy. Nor did it cite borrowing costs, Powell or the strong US dollar. None of the business executives who were quoted in the survey blamed those issues.

Many of them are complaining about something else: the US-China trade war.

"The tariffs have caused much confusion in the industry," one electrical equipment, appliance and components manufacturer said.

A food, beverage and tobacco products executive said: "Chinese tariffs going up are hurting our business. Most of the materials are not made in the US and made only in China."

Blaming the Fed is 'completely wrong'

The trade war between the world's two largest economies is slowing global trade and raising the cost of goods. That, in turn, is sapping demand for manufactured products.

The on-again, off-again nature of the trade battle is also sparking deep uncertainty. Unclear about how long tariffs will last or how high they will go, business owners have dialed back spending and overhauled supply chains. That uncertainty shock is further eroding demand for manufactured goods.

Not surprisingly, economists and market analysts similarly pinned the bulk of the blame on the trade war, and not the Fed.

"We have now tariffed our way into a manufacturing recession in the US and globally," Peter Boockvar, chief investment officer at Bleakely Advisory Group, wrote in a note to clients on Tuesday.

"What is the ultimate cause of all of this? It's the trade war," Ethan Harris, head of global economics at Bank of America, told CNN Business. "This whole narrative about the Fed being too slow is completely wrong. The Fed has never moved faster."

The ISM report provides stark evidence of the trade war's fallout. Not only did manufacturing activity dip further into contraction territory in September, but it was the weakest month since June 2009, the final month of the Great Recession.

Fifteen manufacturing industries contracted in September, including apparel, leather & allied products, printing and related support activities and wood products. New export orders, a trade-sensitive component of the report, had its weakest reading since March 2009.

That's not to say there aren't legitimate gripes over China's trade policy. Business leaders have long complained about the theft of intellectual property and non-tariff trade barriers they say do real harm to American companies. But the trade war is clearly hurting the economy.

US manufacturers are also getting dinged by the global economic slowdown. Major economies including China, India, South Korea and Germany have stumbled in recent quarters. That global slowdown is being amplified by the trade war.

"It's all a vicious circle," said Alec Young, managing director of global markets research at FTSE Russell.

Strong dollar isn't helping. But it's not the main problem

Trump is correct to say that the dollar is strong. The US dollar index, which measures the dollar against a basket of currencies, hasn't been this high since the spring of 2017.

But while a strong dollar is great for Americans touring overseas, it makes it harder for US companies to export their goods. Everything from iPhones, tractors and cars get more expensive for foreign buyers. And then multinational companies get dinged when they convert their foreign sales back into dollars.

"The strong dollar is a headwind. But it's not the end of the world," said Young.

Trump argued that the Fed deserved the blame for the strong dollar because America has higher interest rates than many other major economies.

But Bank of America's Harris said it is the trade war, not the Fed, that is causing the dollar's strength. Nervous about the global economic slowdown and trade policy, investors are dumping foreign currencies in favor of the greenback.

"The Fed is the thing that has really helped cushion the blow of the trade war. They have been preventing the dollar from being even stronger," said Harris.

The Fed, citing the trade war and global slowdown, lowered interest rates twice this summer — the first such cuts since 2008.

Rate cuts are a blunt tool. Cheaper borrowing costs help interest-sensitive sectors, such as housing and autos. But the cost of capital is already near record lows. A discount on borrowing costs won't do much to clear up the uncertainty and supply chain havoc wreaked by the trade war.

"The only reasons anyone cares about the Fed is because we can't get a trade deal. The Fed is an insurance policy," said Young, of FTSE Russell. "What Wall Street wants is an end to tariffs."

Can households keep propping up growth?

Recent history shows that the United States can avoid a recession even when the ISM manufacturing index drops into contraction territory. That happened multiple times in the 1990s as well as in 2003, 2012, 2013 and in 2016, according to Bespoke Investment Group. That's because manufacturing only makes up a small part of the modern economy.

Consumer spending, which drives about two-thirds of the economy, remains solid because unemployment is low, confidence is strong and US stocks are trading near record highs.

The hope is that consumers will continue to prop things up, extending the longest economic expansion in American history.

And it's still possible that Washington and Beijing, fearing economic trouble, finally reach an agreement to avert another round of tariffs that would damage growth. A trade deal, especially one that rolls back existing tariffs, would boost confidence among CEOs and households.

But some "cracks" are starting to show in consumer spending, according to Lisa Shalett, chief investment officer at Morgan Stanley Wealth Management.

In a report to clients, she noted that hiring has slowed, personal spending decelerated in September, and consumer confidence in the availability of jobs tumbled.

The risk is that the consumer picture could darken before a trade agreement can be reached.

"If consumers' confidence seriously falters," Ian Shepherdson, chief economist at Pantheon Macroeconomics wrote on Tuesday, "the US could tip into the first recession ever caused directly by the actions of the President, rather than the action of tight monetary policy on an overstretched private sector."

Or as, Bleakley Advisory Group's Boockvar put it, "using tariffs as the tool to push back against China was a really dumb idea and history will not look kindly upon the strategy."

No wonder the White House is shifting the blame on the Fed.