You have to account for the fact that there might not be enough records to assign, i.e. the quantity requested might be too large. A few changes to the code can look after that:
Code:
rs1 = Select * From AssignmentTable Where Priority = '" & Me.Priority & "' And nz([Attempted Calls],0) = 0" ' because it might be Null or 0
rs1.MoveFirst
x = 1
While x <= me!Quantity and not rs1.EOF
rs1.Edit
rs1!CID = me!CID
rs1.Update
x = x + 1
rs1.Movenext ' advance to the next record
Wend
This assumes that you don't really care which records are assigned; Access will not put the results into rs1 in any particular order.