Poinsettias didn't arrive in the United States until 1825. The National Poinsettia Day is celebrated on Dec. 12 in the US, honoring both the plant and the man who brought it to America [source: University of Illinois].
Named after Joel Roberts Poinsett, first United States ambassador to Mexico and the amateur botanist who introduced the plant to the U.S. in 1825, the poinsettia is also known as Mexican Flame Leaf, Winter Rose, Noche Buena and, in Turkey, Atakurk's Flower, because it was the favorite flower of Atakurk, the founder of modern Turkey. - Meaning & Symbolism of Poinsettias
As for the origins of the poinsettias association with Christmas, this should help:
There is an old Mexican legend (16th century) about how Poinsettias and Christmas come together, it goes like this:
There was once a poor Mexican girl called Pepita who had no present to give the the baby Jesus at the Christmas Eve Services. As Pepita walked to the chapel, sadly, her cousin Pedro tried to cheer her up.
'Pepita', he said "I'm sure that even the smallest gift, given by someone who loves him will make Jesus happy."
Pepita didn't know what she could give, so she picked a small handful of weeds from the roadside and made them into a a small bouquet. She felt embarrassed because she could only give this small present to Jesus. As she walked through the chapel to the altar, she remembered what Pedro had said. She began to feel better, knelt down and put the bouquet at the bottom of the nativity scene. Suddenly, the bouquet of weeds burst into bright red flowers, and everyone who saw them were sure they had seen a miracle. From that day on, the bright red flowers were known as the 'Flores de Noche Buena', or 'Flowers of the Holy Night'.
The shape of the poinsettia flower and leaves are sometimes thought as a symbol of the Star of Bethlehem which led the Wise Men to Jesus. The red colored leaves symbolize the blood of Christ. The white leaves represent his purity. - Poinsettias at Christmas