The surprise move by the White House to give thousands of Venezuelans in the Big Apple the ability to work has left City Hall scrambling — as members of the City Council sounded the alarm that NYC isn’t ready to take on another federal chore.

The Biden Administration has promised just 50 staffers to help New York process employment permit applications for the roughly 10,000 migrants from the South American country — and its not clear how many staffers have even arrived to start the job.

At the same time, Gov. Hochul promised to pull together 70 staffers from various state agencies to help — but it was later revealed they were only tasked with making phone calls to migrants.

“We’re figuring this out in real-time,” a City Hall official told The Post when asked about the next steps.

The chaotic situation has also left Venezuelan asylum seekers in NYC confused about what to do.

“We didn’t know that we can now apply to work legally, so tomorrow we’re going to start seeing what the process is like,” said William Bermudez, 43, who has been here for four months with their two sons.

“If I could get a work permit, I could get proper job, which would make things a little better for us,” he said, adding he was willing to work in a restaurant after fleeing Venezuela where he worked as as senior technician.

The Biden administration dropped the news late Wednesday evening about the new status for Venezuelans without much as a heads-up to the Adams administration, according to sources.

Under the change, migrants from that nation — where the rule of leader  Nicolás Maduro has been marked with hyperinflation and starvation — have been given temporary protective status as long as they arrived in the United States before July 31.

This will give those eligible Venezuelans the right to work, but first they have to be processed, which some fear will be a bureaucratic nightmare.

“It’s not going to happen overnight,” one federal source said.

Asylum seekers in the Big Apple, as well, were trying to figure out the opaque process — with one even trying to get some information on the bureaucracy from a Post reporter.

“How do you apply for the work permit?” said one immigrant from the nation, 43-year-old Jose, as he sat on his unlicensed motorized scooter while on a break from the under-the-table Uber Eats delivery gig he already had.

City Hall spokesperson Fabien Levy was unable to answer any specifics on how what city planned to handle the added task.

“We’re going to figure all that out,” he said, adding it depended on how long it took the feds to officially make the designation.

Councilwoman Gale Brewer (D-Manhattan) laughed when asked if the city was ready to handle the crush of paperwork.

“When are they ready for anything? It used to be up to the feds, now it’s up to us to do it.”

After a work application is filed, DHS said it takes about four to six weeks to process the paperwork.

While Hochul seemingly took a victory lap following the news, Adams had a much more pessimistic response Thursday.

“We need to be clear where we are… it’s an important step for the 15,000 [Venezuelans] but… we have 60,000 in our care,” the mayor said on CNN.

Adams later said that figure was even smaller adding up to just under 10,000, while the remaining were kids.

Minority Leader Joe Borelli remarked that this news will reveal who just handed their hand out for money or thought this was a solution.

“They said this is what would lead to the decommissioning of shelters so now that the Democrats go their way, when someone gets their working papers, I hope it comes with a 60-day eviction notice,” he said.

Other Venezuelans who spoke to the Post Thursday were unaware of the news that they could file to work legally starting Oct. 1.

Eduardo Henquelberth, 36, who looked lost as he sat outside 26 Federal Plaza, told The Post he didn’t even know how to apply for asylum — let alone if he knew about yesterday’s news.

“I’m trying to apply for asylum but I don’t know how. I came here [Javits Federal Office Building] with my family to apply for asylum and they told us to come back at 4 a.m.,” Henquelberth said, describing the already confusing process.

Additional reporting by Carl Campanile