What is the definition of a “quorum” in their state constitution?
Per the MN Constitution:
Sec. 13. Quorum.A majority of each house constitutes a quorum to transact business, but a smaller number may adjourn from day to day and compel the attendance of absent members in the manner and under the penalties it may provide.
A quorum is a simple majority. It does not define the population used to compute a majority, but it is easy to assume that it would be members in office and Not total possible members.
Thus 67 is a simple majority and the Republicans would be correct.
Yes, a majority of members, not of seats. At present there are only 133 members. Thus the 67 Republicans constitute a majority.