I do not believe it is possible that the Sabbath day today, could be any other day than the seventh day.
Firstly, the Most High, designated the seventh day as His holy day in Genesis 2:2-3. It is a hard thing to believe that the Lord's will can be subverted.
Yes, individuals can make void the Lord's commands in their lives and that of their community:
Psalm 119:126 - It is time for thee, LORD, to work: for they have made void thy law.
As you see, David has confidence that the Lord will not allow that work to stand--that the Lord will go "to work" to reverse anything that would "make void" his law.
The Lord himself declares that no one can void His words (commands):
Isaiah 55:11 - So shall my word be that goeth forth out of my mouth: it shall not return unto me void, but it shall accomplish that which I please, and it shall prosper [in the thing] whereto I sent it.
and that He is sovereign:
Isaiah 46:9 - Remember the former things of old: for I am G-d, and there is none else; I am G-d, and there is none like me, Declaring the end from the beginning, and from ancient times the things that are not yet done, saying, My counsel shall stand, and I will do all my pleasure.
Isaiah 14:27 - For the LORD of hosts hath purposed, and who shall disannul [it]? and his hand [is] stretched out, and who shall turn it back?
The time the Lord sanctified at creation could not be unsanctified by man. The Sabbath is not a utensil. Time is not an object (physical), nor can it be destroyed, unless by the Lord's will. (I make this point because the Temple, the Holy of Holies, the furnishings of the Temple, the Ark, the Tablets, Menorah, etc. are either missing or destroyed; never-the-less, time is created by no man, cannot be sanctified by man or destroyed by man--or lost for that matter. Time goes one in its God-given ordinances, day-after-day and outside of man's reach).
Man's pagan calendars have changed over the millennia. But the Lord did not pattern His week and his calendar along man's faulty patterns. There is the Sabbath and there are the days leading to the Sabbath. There is only a 7 day week (established at creation) and no man-made "weeks" have ever been successful at overthrowing it. The French tried a 10-day week and the Soviets a 5-day week--both gone. The names of the days have changed. The dating has changed. The new year has changed. But all this is temporary until another crazy idea gains ascendancy. Now, according to the ISO, Sunday is the seventh day. But does this affect G-d's ordinances? No.
Lastly, I have no reference for this, it is beyond the scope of my imagination that the people of Israel, as a community could mess this up. I can forget what day it is today (do it all the time); but the entire Jewish community--worldwide, forgetting for so long that they can't recover? Did Daniel, Ezra, Nehemiah and Zerubbabel (etc.) forget to keep track while in captivity? Surely not.
All one needs to keep a calendar is a piece of leather or stick and a knife to notch it. Surely hundreds of thousands--millions of people could rely on the community to self-correct.