It seems that maybe she wasn't all that poly to begin with or perhaps has some unspoken fears/reservations about the lifestyle. Maybe it's because she isn't involved with anyone at the moment...but whatever her motives are, you need to have a frank and open discussion about it with her.
Does she know how much of yourself you'll be giving up to be mono and how much it hurts you? Perhaps she would reconsider her request if she knew...
Please don't make decisions based on fear or ultimatums...because you'll likely regret them down the road. Marrying her and promising monogamy when you're feeling pressured and unhappy is dishonest and it's setting you up for failure.
I would never ask either of my loves to deny any part of who they are to be with me. I accept them and hope for the same in return.
I tried being reasonable. I didn't like it. ~Clint Eastwood~