First, the inflation report --
https://finance.yahoo.com/news/live/stock-market-today-sp-500-nasdaq-soar-lead-dow-higher-as-senate-vote-lifts-hopes-for-end-to-us-shutdown-210042449.html
Scroll, scroll, and scroll down to the one, "The government shutdown could end soon. The release of key government data could take longer."
"There will likely NOT be an inflation release next month for the first time in history," a White House account posted on Oct. 24, saying it was because "surveyors cannot deploy to the field depriving us of critical data." ((the all-caps "NOT" is in the original, but the highlighting of the date is mine -progree))
From the OP's article on jobs data, link repeated for convenience of reference --
https://www.cnbc.com/2025/11/12/white-house-october-data-release.html
On the issue of data collection, Goldmans economists said they expect the shutdown to have a limited impact on the quality of jobs data.
As for timing, Citigroup economists on Wednesday speculated that the September nonfarm payrolls report could be released as early as Friday but more likely in the early part of next week. They said it could take until early December to put together the October count.
Jobs report data should be easy to collect belatedly because it involves asking business for hard numbers, according to Jeffrey Roach, chief economist at LPL Financial. In fact, he said the BLS could likely get multiple months worth of data during one collection period if needed. ((speaking of the headline non-farm payroll jobs numbers which comes from the Establishment Survey of businesses -progree))
But he said its harder to get information from everyday people because it requires asking them about their willingness to work during a period that has already passed. ((speaking of the separate Household Survey, which is the basis of the headline unemployment rate and labor force and labor force participation rate among many other metrics --progree))
Its just the more nuanced qualitative surveys that cannot be replicated, Roach said. The water has gone under that bridge already.
If the Establishment Survey numbers are bad, as pat_k suggests, due to fork-in-the-road federal employees being let go, they may very well come up with excuses for not putting out any of the October jobs report. But that's just kicking the can down the road -- any upcoming November and December etc. job reports will show fewer federal workers, so that can't be buried forever without gamesmanship.