God's entire plan of salvation could have been derailed by a petulant girl? It's good he didn't catch her at that time of the month! At any rate, Mary did not have this option. Her decision (and all things pertaining to Christ) were foreordained by God and guided by His omnipotent will.
Acts 2
22 "Men of Israel, listen to these words: Jesus the
Nazarene, a man attested to you by God with miracles
and wonders and signs which God performed through Him
in your midst, just as you yourselves know--
23 this Man, delivered over by the predetermined plan
and foreknowledge of God, you nailed to a
cross by the hands of godless men and put Him to
death.
24 "But God raised Him up again, putting an end to the
agony of death, since it was impossible for Him to
be held in its power.