According to this news report, Obama will present the Holy Father with a priestly stole worn by St. John Neumann. However, there's no possible way the pictured stole is from the 19th century.
Here is the stole pictured at CNA:
That looks like an Almy stole, designed to hang straight down. There's no way that a 100 year + liturgical vestiment would look that well preserved, unless it has been encased in an airtight box.
Now compare that to an authentic 19th century vestment set:
Notice the stole hanging to the left and how it flares out at the ends. Here is a modern stole based on this pattern:
According to the news article: "The stole was discovered by Louis DiCocco, president of the St. Jude Shops and the St. Jude Liturgical Arts Studio, who was contacted by the Obama administration for assistance in finding a gift for Pope Benedict."
Mr. DiCocco should come clean about where he discovered this stole. Maybe online from Almy? See this picture from Almy's website:
Please note that it appears Mr. DiCocco ordered the white stole.