President Donald Trump speaks during the ceremony to present the Commander in Chief's Trophy during a White House event with the Army Black Knights in the Rose Garden.

The CNBC All-America Economic Survey finds either majorities or pluralities of the public say they don't care for tariffs against China, don't approve of Trump's handling of the Chinese trade negotiations and don't even care if a product is made in China. Most say they don't even see China as an economic threat.

"The notion that China is this massive economic monster that the U.S. has to contend with has clearly not permeated the public the way the Trump administration wants it to or thinks it has," said Hart Research Associates' Jay Campbell, Democratic pollster for the survey.

The survey finds Trump's trade policies have not cost him much in the way of support. It shows 40% of the public approves of the job the president is doing overall, with 50% disapproving, mostly unchanged from the March survey. The quarterly survey of 800 Americans nationwide has a margin of error of plus or minus 3.5 percentage points. The survey took place between May 22 and May 26, before Trump threatened to slap tariffs on Mexican imports.

Meanwhile 48% of the public approves of the job Trump is doing handling the economy, with 43% disapproving, largely unchanged from last quarter. But that's not the case for views on how the president handles trade negotiations with other countries, where 37% approve, 43% disapprove and 16% offer no opinion.

The numbers are worse for the president's border security and immigration policies, with 37% approving and 50% disapproving. They are about as bad again for Trump's handling of the U.S. relationship with China, with just 32% approving and 45% disapproving.

The Republican pollster for the survey, Micah Roberts of Public Opinion Strategies, says the data shows strong GOP support for the president overall and on the economy. But that support falls off by 20 to 30 percentage points on most of the president's trade policies, Roberts said.

Despite all the anti-China rhetoric from the administration, and retaliatory Chinese tariffs, just 34% say they are less likely to buy a product if it has a "Made in China" label. In 2007, when CNBC first asked the question, 52% cared. Now 57% say they don't care, up from 39% who said they didn't care in 2007.

Meanwhile, just 32% see China as an economic threat, up a bit from 25% in June, but down substantially from 49% in March 2016.

Negative views on trade take place against upbeat views on the economy. A 52% majority of Americans think the job market is better than it was two years ago, and a 39% plurality believe the housing market in their area has improved. A post-recession record 47% believe their wages will rise in the next year.

Stock market optimism among those surveyed has recovered but has yet to rise to the lofty levels of last fall. According to the survey, 41% of the public say now is a good time to invest, compared with 32% who say it's a bad time. The 9-point difference contrasts with a 26-point edge for optimism in October and a 17-point edge during most of the Trump administration.