The role of the Fed

Money market mutual funds receive the reverse repurchase agreement, a.k.a. the reverse repo rate, for funds held by the Fed overnight, so it functions as a rough floor on yields.

That rate stands at 0.8 percent. It was close to zero for many months. 

At the moment, short-term Treasury bills, with yields in the 0.85 - 1.05 percent range, provide a practical ceiling for funds that hold government securities.

If the operating expenses of money market funds exceed the income they bring in, the funds could theoretically pay negative yields.