Did the Obama administration send troops to the Russian border?

Answer 1

No. There would have been a response from Russia if United States troops were on their border. The closest we are to Russia would be Poland which is a NATO country and is a buffer between Eastern Europe and Central Europe.

Answer 2

Not in order to directly threaten or fight Russia. But the USA did participate in NATO excercises in the Baltic countries that used to be part of the USSR and that border on today's Russia.