An executive order won’t kill the bill. It is totally separate from the legislation. The legislation stands on it’s own with or without an executive order or reconcilliation in the senate.
I don’t think a guarantee from the POTUS that he will issue an executive order to veto the part of the bill he doesn’t like (particularly in exchange for votes from Congress) is constitutional. Unless this is the cover Stupak wants and no such order will be issued. Just my opinion, but I will listen to those who are smarter than me on this.