In "Gift of the Magi" the main complication stems from the impoverishment of the young couple; Della and Jim simply do not have enough money to purchase Chirstmas gifts for each other. This problem is suggested in the exposition of O. Henry's poignant story:
The "Dillingham" had been flung to the breeze during a former period of prosperity when its possessor was being paid thirty dollars per week. Now when the income was shrunk to twenty dollars, the letter of 'Dillingham' looked blurred, as though they were thinking seriously of contracting to a modest and unassuming D.
Also in the exposition, Della cries after counting her meager one dollar and eighty-seven cents which will not pay for the beautiful watch fob which she desires to give her husband for a Christmas present.
The resulting rising action that comes from this original complication gives rise to Della's inner conflict of cutting her hair which Jim loves and of which she is so proud. Jim, too, suffers from inner conflicts resulting from the complication of penury as he wrestles with the idea of selling his gold watch to buy the beautiful combs for his wife's Christmas present.
A touching plot, indeed--and relevant today in this material world-- the story,"The Gift of the Magi," has a resolution to this complication that many would do well to ponder. As O. Henry remarks, "They [Della and Jim] are the wisest of all."