Mark 13:20 “If the Lord had not cut short those days, no one would survive. But for the sake of the elect, whom he has chosen, he has shortened them. 21 At that time if anyone says to you, ‘Look, here is the Messiah!’ or, ‘Look, there he is!’ do not believe it. 22 For false messiahs and false prophets will appear and perform signs and wonders to deceive, if possible, even the elect. 23 So be on your guard; I have told you everything ahead of time.
The only thing the non-Calvinist can do is completely redefine what it means to "choose" and to "predetermine" in reference to God.
I just sent this in a PM and I'll post it here:
If one believes the Isrealites were God's chosen people, but that he chose them because they choose him first, then all that is happening is God is going along with what the Israelites had already determined they were going to do.
That is no different from salvation as a rule. If God chooses us because we were going to choose him, then all God is doing is looking to the future, as if examining a film strip, and approving what is going to happen.