Final Result: The 117th Congress did actually meet and swear in on a Sunday, January 3, 2021. Per the other answer by @NateEldredge, this was the first Sunday swearing in for at least several decades.
December Update: There still does not appear to be a bill to change the date of convening the 117th Congress. However, an entry in the Congressional Record for December 20, 2020 states this:
Mr. GRASSLEY. Mr. President, today is Sunday, and I want to remember
what Senator Byrd said on a lot of Sundays when the Senate was in
session. He didn't say this because he didn't want to work on Sunday,
but he wanted everybody to remember the significance of Sunday for some
people, particularly Christians. He always said: ``Remember the Sabbath
and keep it holy.''
Now, I want to refer to another particular Sunday. Never in the
Senate's history has the Senate convened Congress -- meaning a new
Congress -- on a Sunday. The Constitution mandates that Congress convene
at noon on January 3, unless the preceding Congress, by law, designates
a different day.
Of course, January 3 has fallen on a Sunday over the last 238 years,
and each time, by unanimous consent, the Congress set a new convening
day other than that Sunday. So now it appears, for the first time in
history, that Senate Democrats don't want to agree to such unanimous
consent and instead are insisting that the Senate start the 117th
Congress on Sunday.
I am not looking to get out of work. I have proven that I have
respect for attendance in the Senate. But out of respect, the Senate
usually does not have business on religious holidays observed by
members of various faiths.
So just like Senator Byrd, I also think the Lord's Day, particularly
when it is paired with the weight of starting a new Congress, deserves
If Senator Grassley is correct, then all previous Congresses never allowed the convening date to fall on a Sunday. Although there do not appear to be any bills formally introduced yet for the convening of the 117th Congress, his remarks above suggest that there has at least been discussion of the issue, and he accuses Senate Democrats of preventing the change of date.