Nephi and Mary

With Christmas time coming around the corner. I want to post a question to see others views on the subject. Do the prayers of Nephi determine the day that Mary gave birth to Christ? Let me expound.

We read in Helaman 14:3-5 that Samuel the Lamanite prophecies the signs of Christ birth on the American continent. Now here is 3 Nephi 1: 9-13

9 Now it came to pass that there was a day set apart by the unbelievers , that all those who believed in those traditions should be put to death except the sign should come to pass, which had been given by Samuel the prophet.

10 Now it came to pass that when Nephi, the son of Nephi, saw this wickedness of his people, his heart was exceedingly sorrowful.

11 And it came to pass that he went out and bowed himself down upon the earth, and cried mightily to his God in behalf of his people, yea, those who were about to be destroyed because of their faith in the tradition of their fathers.

12 And it came to pass that he cried mightily unto the Lord all that day; and behold, the voice of the Lord came unto him, saying:

13 Lift up your head and be of good cheer; for behold, the time is at hand, and on this night shall the sign be given, and on the morrow come I into the world, to show unto the world that I will fulfil all that which I have caused to be spoken by the mouth of my holy prophets.

This story gives me the impression that Nephi prayed for his people so they wouldn’t be put to death, and than the sign came that very night. Back in Bethlehem all I can find to back this hypothesize up is “And so it was, that, while they were there, the days were accomplished that she should be delivered” Luke 2:6

Did Nephi’s prayers “accomplish” what need to be done to cause Mary to go into labor and give birth to Christ? Or if Nephi had not prayed would the signs have come anyway and the people been spared regardless? Or were the signs in the American completely unrelated to the actual birth of Christ?