Many of the Scriptures I have used in discussing the Saturday and Sunday arguements (in previous posts) could be used here. But I'll refrain from using most of them as I have presented this argument to some degree in refuting the other 2 arguments. However some will be used.
Exo 20:9-10 "Six days shall you labour, and do all your work: But the seventh day is the Sabbath of the LORD your God: in it you shall not do any work, you, nor your son, nor your daughter, your manservant, nor your maidservant, nor your cattle, nor your stranger that is within your gates"
This states that 6 days (it doesn't state which 6 days) you should do any work you need to do. And then on the seventh you should rest from such physical labours and honour as a Sabbath day (again, no mention of it being compulsory to select a specific day of the week to do this on).
Another argument is that if God were fussy about which actual day of the week was to be observed why didn't he make it clear, like all the other commandments. God has gone to great lengths to explain which foods were not to be eaten. He went to great lengths to explain priestly duties. He went into so much detail as to how to treat lepers. The tabernacle specifics go on and on. He has explained the different penalties for murder depending. He has explained in detail who not to marry in the family. And I could go on. So are we to believe that he made such a serious oversight as to not make it plain which day he was insistent that we have our Sabbath on?
Along with this comes the question that if it was a particular day of the week that had to be observed or else, why didn't he make some sign turn up on that day each week so there would be no confusion? That way no one would have an excuse to confuse it. And that way all would know what he wanted them to do. He could have made it that the sky goes purple once a week through some strange phenomenon.
The next point is, did God rest on a Saturday? This would be pure speculation to conclude that we know he did. Our sun (from which we draw our night and day periods) wasn't even created until the fourth day of creation (Genesis 1:16-19). The scriptures tell us that a day with God is as a thousand years (2 Peter 3:8, and this is demonstrated in the days mentioned in some revelations which took that many thousand years to occur). So if this applies here then he rested for a thousand years which included every day of the week.
The next point in this same vein is, "which day was even observed by Israel initially" (when the law was received by Moses)? Again we have no scriptural support for any specific day. But one thing bears keeping in mind if anyone claims they know for sure that it was a specific day; Israel spent many years in captivity through worshipping idols, and left the following of God many times anyway. Are we to believe that on all these occasions they even considered to begin holding their sabbath day on the day of the week they used to observe, when they finally returned to worshipping God? They would naturally work six days and rest on the seventh, as commanded, from that day (whatever day it was).
Nowhere in scripture is anyone commanded to observe any specific day of the week. There is no certainty whatsoever as to what day God rested on after creation. There is no certainty what day Moses originally got Isreal to rest on. There is no foundation for a debate on what day of the week God insists on us having as a Sabbath. God has made no such insistence. This is the leaven of the Pharisees Christ warned against: Doctrine invented by man. It is trying to strain at a gnat while swallowing a camel. What matters is how you observe your Sabbath day, not when. Don't get sucked into believing such things to be doctrines of God.