Why do you think delegates to the constitutional convention might have had a difficult time deciding how to choose the president and vice president?

There are a number of things that influenced the problem of electing the president at the constitutional convention:

1) the lack of established politicians and political parties in the US at the time - the person chosen would not have been a well-known politician whose views are predictible

2) they remembered the absolute rule of the English king, so they were worried the new president could also be a dictator - they wanted to make sure that the president was chosen in fair election and could be removed from the office if necessary