I think it's highly likely we won't have a national vaccine mandate as we enter the New Year of 2022. The government has read the mood of a vocal minority in the country, and delayed the implementation date of much of the mandate until January 4th. The government knew it's mandate would create a disaster scenario for the holiday season. It will never admit the mandate was a mistake. But by January, the government will be able to claim that along with the development of new medications the mandate created additional vaccinations that reduced or eliminated the need for a mandate. So it will claim that it is "following the science" which would actually be a first in the pandemic. The President will be able to claim victory over the pandemic. That will likely work out as well as a previous President proclamation from an aircraft carrier that we had won the Iraq war.
The lesson, in case we need reminding, is that the federal government has become a bloated bureaucracy that will never admit its mistakes. And we can tell a governmental directive is a mistake when ordinary citizens are conscripted to enforce it, because the government's own law enforcement personnel know it's too dangerous.