Hi Brother...
I don't think that we are confined to a day of the week for which we meet together. In fact, I don't think that we are confined to a day at all for which we fellowship, as the early Church met daily in one another's homes.
Those who adhere to a specific "7th day Sabbath" mostly, as far as I can tell, feel that they are still prohibited to work on that day and should remember the finished work of the Lord's creation...period. There is nothing in the Word that dictates WHEN we meet together with believers in Word or worship. In fact, the oft-quoted verse pertaining to "going to Church" -- Hebrews 10:25 -- actually speaks about meeting together even more frequently as we see "that day approaching." Interestingly, that passage even lays down a motive for meeting together: ENCOURAGEMENT.
There are many believers who don't adhere to a set of requirements regarding the Sabbath. Many of us see each day as a "Sabbath day" in which we recognize and remember the finished work of God (from both Creation and the Cross). For many of us, we feel that we are fulfilling the initial sanctity of the day by spiritually resting and remembering Christ every single day. Regardless, there simply are not any set of [i]requirements[/i] about when to meet in the New Testament. I suppose that Saturday and/or Sunday are/is just as good as any day simply because most people are off of work anyway.
When I was an undergraduate student, however, the most blessed days were on Mondays as I met in my dorm with other sincere believers. We broke bread (spiritually and physically), prayed and encouraged one another as we walked through the wilderness of this world in a university. I actually received more encouragement during those intimate prayer meetings/Bible studies than I did during most of the Church services that I have attended.
:-)