Do couples behave in such way these days as Jim and Della in "The Gift of the Magi"?no
Your question is a matter of opinion. The special love that Jim and Della have for each other which is founded on their willingness to sacrifice their most precious and treasured material possessions for each other does exist, I imagine. It is difficult to answer this type of question because one cannot know with any degree of certainty the intimate details of any real life couple's relationship.
Everyday people constantly make sacrifices for each other, but it is difficult to make an exact comparison to the story that O Henry wrote to illustrate the nature of love in a pure form.
Although the time period in which O Henry sets the story predates the women's movement and therefore places clearly defined and limiting roles on women. Della has no opportunity to earn money to buy her husband a gift, therefore, she is left with few options. Selling her hair is her only opportunity to legitimately earn money on her own. She does not have a job, and that is probably because socially speaking, she is meant to remain at home.
Women have many more opportunities today then when O Henry wrote this story, but I believe that the type of love that he wrote about does exist.