The number of Americans filing for unemployment benefits jumped to its highest level in two years for the week ending March 14, but that was nothing compared to the absolutely historic wave of job losses economists see coming.

The state of play: Goldman Sachs predicts that more than 2 million Americans will file for unemployment claims by next week, pointing to "an unprecedented surge in layoffs this week."

The upcoming March 15-21 period is expected to see "the largest increase in initial jobless claims and the highest level on record."

If Goldman's economic forecasters are right, the number of Americans filing initial claims for unemployment benefits next week will more than triple the all-time high of 695,000 set in October 1982, and nearly four times the number seen at the peak of the Great Recession.

The numbers are expected to be so bad the Trump administration has asked states to hold off on releasing them before Thursday, according to a Wall Street Journal report, citing an email from a U.S. Labor Department official.

Data: U.S. Employment and Training Administration via Federal Reserve Bank of St. Louis; Chart: Andrew Witherspoon/Axios

The big picture: Thursday's jobless claims report is likely "only the tip of the iceberg: These numbers do not account for the surge of new claims from overwhelmed [unemployment] websites from coast to coast," Andrew Stettner, senior fellow at the Century Foundation and an expert on unemployment, told CBSNews.

To wit, New York, home to 463,000 workers in the food and hospitality sector as of 2018, saw a 17,000 net decline in unemployment filings last week.

One level deeper: Based on anecdotes from a wide range of business contacts, Goldman's economic research team foresees "an unprecedented decline in revenues across many industries."

"Consumer spending on sports and entertainment, hotels, restaurants, and public transportation in particular have already dropped dramatically."

Another perspective: Analysts at Bank of America Global Research expect a slower jobs drip, with the U.S. economy losing 1 million jobs a month.

"We expect a total of approximately 3.5 million jobs will be lost," BofA strategists said in a note to clients before the release of the Labor Department's initial jobless claims report.

They see the unemployment rate rising to 6.3%, hitting the leisure & hospitality and retail industries the hardest.

"These sectors have a high share of hourly workers - about 80% for the former and 70% for the latter. And these workers struggle to work from home. This means they are vulnerable to a reduction in hours worked and likely outright job cuts."

Go deeper: The coronavirus economic pain in the U.S. has begun