“The consumer’s really the star of the show right now, and if you were to see any signs of a break there, it would be significant,” Mr. Stanley said.

Downturns in consumer sentiment don’t always translate into cutbacks in actual spending. And past shutdowns haven’t done lasting damage to either confidence or spending. Jim O’Sullivan, the chief United States economist for High Frequency Economics, wrote in a research note that the Michigan index also fell in 2013, then bounced back quickly when the government reopened. But he cautioned that the current shutdown had already outlasted any previous one.

Adding to the challenge for forecasters, the shutdown has stopped the release of much government economic data. The Commerce Department, for example, was scheduled to release retail sales figures for December e this week; that report has been put off indefinitely.

“Disentangling what is temporary effects and what is the underlying trend becomes that much more difficult,” said Brett Ryan, an economist with Deutsche Bank in New York. “It just adds more uncertainty during a period when the market’s already skittish.”

In the absence of much hard evidence, economists have been left guessing about the shutdown’s impact. White House economists this week doubled their estimate of the damage being inflicted. The Council of Economic Advisers said the shutdown would reduce quarterly economic growth by 0.13 percentage points for every week that it lasted as federal contractors lost out on work and government employees went without pay.

Some analysts see even bigger potential effects: Deutsche Bank estimated on Thursday that in the worst case, the economy could contract in the first quarter because of an extended shutdown.

Portions of the surveys offered a pointed political warning to Mr. Trump. In the span of a year of SurveyMonkey polling, the president has lost much of the approval he enjoyed with Americans on economic policy. Nearly as many respondents now say his policies are making the economy worse as say they are making the economy better. A year ago, Mr. Trump held a seven-percentage-point advantage on that question.