The MMBFJ111's worst case Vgs(off) is -10V, not -3V, so to get guaranteed hard cut-off you'll need far more negative bias than you are expecting if either its (interchangable) drain or source are near 0V. If you want a JFET that will actually cut-off with -3V on its gate, try MMBFJ113.
I echo Jbb's request for more information on your actual application, and we need the 'big picture' overview, not just the detail of what you think you need to do to solve your immediate problem.