My fiancŽ is coming to marry me in 2012 and wants to bring cash, $20,000 . Will she be able do this and is there any tax on the money

If she is bringing currency notes and travellers checks exceeding US dollars 10,000 she must inform the immigration and customs department on arrival. Customs officer may question her about the source of the money. Also I really doubt Russia will allow her to carry this much cash.
If the money transfer from Russia to US is through banking channel, she does not have any problem.